Spicy.

People already gave good answers. I'll only give some tips.

The general Linux installation practice used to be to separate "/" (root) and the "/home" partitions. For example, I have 30GB for root and 200 GB for Home. The root is where the system is installed. I have always thought that this was the most secure way to do it but then Adam said it is not and I've searched for it and found that it doesn't actually have any good advantages.

So, when installing Linux on your system alongside W10, Make it a single partition. That way you won't have problems with disk space. On my virtual drives, I use 10GB for Mint installations but since you are going to be using it indefinitely and I am sure you'll want to try things out, I would suggest 40 or even 50 GB if you can spare.

CREATE THE PARTITION on Windows 10 and NOT on Linux or live USB. W10 has some aggressive protection issues that can cause problems if you try to modify the disk without its permission. I learned the hard way :)

You can use almost any Linux from USB, at the cost of performance. There is an amazing program called "multibootusb" which not only allows you to use 1 USB for multiple Live OS (including Windows OS), but it also allows you to spare space for that Live OS's use. Normally, when you use a Live USB, the changes you make are lost when you log off. With multiboot USB, you can give up to 4 GB space for the changes and whatever you make becomes persistent.

On Virtual Machines (VMs) on windows 10, I don't think this is a good idea for you. The way VMs work is that the guests (the OS in the VM) uses hosts (the real OS, W10 in your case) resources. So in order to be able to connect to the internet from a VM, the host must also be connected to the internet. As far as I know, there is no other way.

One final note. Linux may be mostly virus free but that doesn't mean it deletes the virus from the files you download. So, if you download an infected file (executable) and then use it on Windows, your windows system will be infected. And then, if you take a file from that windows system and send it to someone else, they may also be infected. Just because you did that transaction via Linux does not prevent that.

2nd Final note. Mint is great. I use it as my primary OS every day. Just set a firewall (which is already installed with Mint) and you are good to go.

When I have more time, I'll tell you about dependencies and packages. Which I believe is the core of Linux's greatness and everyone should atleast have a basic understanding of what it is.

Well that all sounds pretty good for the most part, but for slight clarifications:

A: I don't know why but people seem to differ greatly on how much space they think it will take to install. I saw everything between 2 GB and 40 GB. I was hoping to put it on an 8 GB USB stick.

B: To address two people - first Dark_art_, when you say the files are lost upon shutdown, if I have Linux installed and running on a USB stick then can't I use it as though it were a hard drive? So couldn't I save files onto it and they'll appear in the Linux drive? aRealCyborg, same question. Why would I lose my files if I save them into directories on the USB stick? It can't just automatically erase files, and why would it do that, anyway?

C: I want to clarify that I would like to be able to run this on any arbitrary computer, without knowing ahead of time what hardware is on the computer, and without the need (or in some cases, even the opportunity) to download or install the necessary drivers after booting into the arbitrary computer. For this reason, I really need generic monitor, video card, mouse and keyboard drivers. I think anything else would probably be superfluous. And for that matter, if it didn't have a compatible video card driver then wouldn't I see a black screen or something? Then how could I change or fix the driver, anyway? Dark_art_, are you implying that you were using a nVidia hard drive? I thought they only made video cards and such. Maybe I misunderstand. In any case, whatever generic video card drivers I get, they need to work on all nVidea cards (and other cards as well) preferably with a high resolution limit, but they don't have to support anything fancy, like even OpenGL or anything. It simply needs to be able to show all of the GUI of the OS. But I'll look into Etcher and Rufus, thanks.

D: Also, I thought of one more thing - if I want to make copies of this USB stick then can I just copy the files from one to the other? I get the feeling that it might not recognize the boot record or something, if I did that. Do I need to somehow make it an ISO and then burn it onto another one, or do I have to reinstall Linux and set it up again?

EDIT: I just saw Engerek01's post (I hadn't realized there was another page), and I already know about the VM and virus issues, but thanks for telling me in case I didn't know, because that would have been bad!

Most modern linux distros (especially the assclown ones marketed as easy for windows users) are bloated as all hell. Linux can take anywhere from a few megabytes to tens of gigabytes depending on how much crap you've got. You're not gonna have much fun with them on a 8GB stick.

Here's the thing: when people think "easy for windows users", they think stupid GUIs, eye candy, loads of crappy preinstalled software to mimic the windblows experience. How *could* it be nice and slim? (Well, it could be nice and slim but the vast majority of software devs don't give a shit. There's some slick stuff around, maybe enlightenment and such, but the vast majority of popular gui software is a crumbling tower of bloated dependencies)

Even the linux shell experience (what you find in mainstream distros) is comparatively bloated due to GNU crap and overengineering. 99% of the time, the Linux world chooses more features and more flexibility over something plain and simple. Of course you can save files on a USB stick, assuming there's a writable partition on it for that purpose. The vast majority of drivers on linux are in the kernel so it'll run on any PC with common hardware. Hardware is automatically detected and the right drivers are used. I don't know what's the status of nouveau (open source driver for nvidia gpus), but I imagine you can get modesetting with it on any card that isn't too new. If it doesn't work, you can blame nvidia for being an ass clown company and buy amd/intel next time. Also a few things (some wifi cards for instance) might require additional firmware blobs that may or may not be installed, depending on your distro. Don't copy files, use dd. (Assuming you're working with an image small enough to fit on the stick you're copying, otherwise you'll have to partition, install bootloader, etc.)

Only if one wanted to compartmentalize or plan on taking backup of the whole partition regularly. Then we got lvm (logical volume manager) that is not exactly what I would recommend doing on a home computer as it breaks with KIS, It's more work that the gain on a computer with few disks (and little changes). One basically adds more layers to the system, and if one uses VM or something like Docker on top of that again, one is actually a really really perverse admin :)

The most used filesystems today are very robust so it really doesn't matter anyway.

A typical Mint partition needs way more than that as soon as you start installing programs and updates. And updates need lots of space before installing. At least 20-30 partition is the bare minimum.
The ISO is like a "mirror" of a install system. Using dd will mirror that over to the USB drive. You can do this with this line;

sudo dd if=filename.iso of=/dev/usbdevice bs=8M | sync

if= input file
of= output file

Everything in Linux is considered a file - even folders/devices/hardware.

If you do it on a windows; https://rufus.ie/

That is not a problem. If the install ISO is 2.5GB is will use roughly the same on an USB stick (for install purposes).

Just make sure the partition you're installing to is much much bigger (that's where the 30-40GB comes in).

Sorry if my post was a little confusing, to clarify:
You can run Linux Mint on a USB stick in 2 ways, live mode and installed mode. Both will run in pretty much any computer.

As the name implies, installed mode is just Linux Mint installed on a pen drive, you can run it on pretty much any computer while keeping your files (typical instalation requires one pen drive to install Mint and another one to receive the install of Mint, there are way to do only with 1 pendrive though).

Live mode is when you make a pen drive with the ISO downloaded from Mint website. You use this pen drive to try Mint, without keeping any files and then decide if you wat to install it or not, you need to Run Mint in Live mode in order to install it later, if you want. I mention it because if you want anonimity, this mode keep no files after shutdown.

Can't be easy for you, trying to understand all this bluberish... This may sound very confusing but is not, is very simple. If you have a USB pen drive laying around, just try it, will take less time to try it than to write a message here.

Steps: Go to Linux Mint website and download any version (I use Cinnamon)
Download Balena Etcher (me uses portable version)
Open Etcher and flash the pen drive with Mint Iso
Boot your computer from USB and voila, Mint is running on Live mode. Will not install nothing at this time neither touch your hard drive. This will answer many of the questions and you can decide if you like it or not :D

clarry, when you say I'm not going to have much fun with an 8 GB stick, I'm not sure what you mean. As I said, the ONLY thing I intend to do in Linux is use the Internet, and I really don't need any space at all, beyond what the OS uses. I don't need all that extra software either, but I don't care whether it's there, as long as it doesn't hurt anything, and it all fits on the USB stick. The thing about drivers is that I won't necessarily know what hardware I need it for. The point is that I want it to be a portable USB stick that I can stick in any computer, even if I don't know what hardware is on that computer, and boot into Linux, without having or installing or even configuring any drivers. And what's dd?

sanscript, I know you were replying to Dark_art_, but as for my issue, I shouldn't need 20 to 30 GB because like I said, I only need space for the OS and that's all. As for your example command, that looks interesting, but I'll have to look into it. As for you reply to me, I don't see why I need 30 to 40 GB unless the OS takes that much by itself. And it seems that you might be misunderstanding what I have in mind. I want a USB stick that I can plug into my computer, restart and boot into Linux from the stick (NOT the Linux installer but the Linux OS, running on the stick!). And if possible, I'd like it to be an 8 GB stick, and such that if I need to save a file into the directory structure of the Linux OS then it will just end up being stored on the stick with everything else.

Dark_art_, yes, installed mode is what I want! Live mode sounds similar to a version of Linux which I think is called Knoppix or something, and it runs from a CD, but you can't save anything to it (mainly because it's a CD). There are different styles of Mint even? Ugh, do the variations never end? So I guess I'll look into Cinnamon.

Well you can use a 8GB stick but I suspect it's going to be a tight fit with any mainstream distro (unless they offer minimal installs). A truly portable stick is not possible but a generic kernel + all the firmware you can find will do pretty well. dd stands for convert and copy. https://pubs.opengroup.org/onlinepubs/9699919799/utilities/dd.html

Just be careful, as mistyping the command will make you lose data.

In particular, I recommend doing the following:
1. use "lsblk" to see what the block devices are on the system, and identify the USB device (make sure it's not your primary hard drive, or you'll lose data!)
2. Enter the command, but without the sudo in front of it. You might also consider putting a hash sign ("#") at the beginning of the command, which will make the shell treat it as a comment and not actually execute it.
3. Make sure you entered the command correctly, that you entered the correct device, and you did not mix up "if" and "of". (It's easy to mistype that.)
4. Are you *sure* the command is correct? Getting this wrong will cause data loss.
5. *Now* you can add the sudo and/or take off the hash sign, then press enter.
6. You may be prompted for your user password. If you are, then you will need to type it, but this does give you one final chance to make sure you entered the command correctly.

By the way, the risky part here isn't the "dd" command, which is no worse than the "cp" command; it's the "sudo" that makes this risky, as it allows privileged access to the system, including direct access to the hard drive (without going through the filesystem and the kernel's checks, permission and otherwise). If you try to do this without sudo, you will get a "Permission Denied" message, as your normal user can't directly access the hard drive or usb device.

Understand many distros come with a plethora of programs/applications that are not strictly needed for basics, like an office suite and several media players. Dump those and you can easily work from an 8GiB USB stick.

It's been a while since I last checked it, so I just installed Linux Mint 19.3 on a 16Gb pen drive, didn't even used the keyboard for that. Took around 10 minutes.
It occupies around 7.5Gb for the full install so it needs a 16Gb USB drive.
Live mode is preciselly that!

Yeah, there is many variations but don't worry, it's not that hard. Most Linux distros (and there are many) are packaged different from Windows. In Windows You get the OS and then install the programs you want. On Linux, most distros are very similar, there are just different themes, start menu and pre-installed programs. Is a little more complicated than that but there's not much a end user like myself need to know about those packages. It just works ™

I see, I haven't done it with that small stick so can't say if it'll work (I usually go with a portable harddrive if I go that road).

In that case you either need two usb sticks (booting the computer from one, and installing to the other), or running the install in Virtualbox (installing directly from the ISO to USB)

EDIT: But choosing to install rather than using the live system might make it slower (and USB stick is usually slower than harrdrive). The live system is often compressed (squashed) into a read-only file, and thus uses more of the memory to work/unpack from.

Yes, I too think a 16GB stick might be better.

Well now I've downloaded the Mint 20 ISO and I've burned it using Rufus (I also checked the hash thing, which didn't work at all the way they said it would, but I managed to figure out how, and tried to authenticate it, which didn't work at all, but I figured out if the file's identical to what it's supposed to be then what could go wrong?). And I used the option for MBR, default FAT32 and 4098 bytes.

During the process it said it was missing something it needed to download, so it downloaded it an then finished. I checked and it seems to have put a bunch of files on the drive (1.8 GB worth), so I figured it was successful.

I restarted and it ignored the drive and just booted into Windows! So I guess one of two things happened: either I somehow burned it the wrong way or something went wrong during the process (though there were no errors), or otherwise maybe my BIOS isn't configured to boot from USB devices or from that particular port or whatever. I specifically said to the computer manufacturer that it must be able to boot from USB, but he probably didn't bother to configure it. Can they typically do that by default? I'm not sure I've ever even checked the BIOS of this computer (it's new and I've never needed to do so) but I guess I'll be doing that. If that doesn't turn out to be the problem then what else could be wrong? I suppose I could also try it on a DVD.

In any case, even after I get that to work, I'm pretty sure these are just the installation files, right? So when I go to install it (if I can get it to actually boot in the first place), and it asks me what drive to install it on, can I just select a USB drive and it will install it there the same way it would install it onto a hard drive, and not care which kind I use?