I'm going to answer to the "Wine or Crossover or Playonlinux" question:
I strongly suggest you to use Wine!
First of all the other 2 software are based on Wine but by using Wine you will probably learn how to use all of them, this is not the case if you use Crossover or Playonlinux.
This happens because Wine is a 'terminal only' software while the other 2 have a graphical interface.
It may sound scary but Wine is easier than someone may think.
That said I think you misunderstood a bit how things works in Wine
One of the biggest issues I have with Linux software is the way it’s needs dependences from a repository. While there is no DRM but getting things to work offline can be tricky and from my experience requires a good understanding of terminal to make it all work. This includes getting dependences from the repository.
It's very unlikely that you need to install something from your distro's repository for a game not working in Wine, especially when using distros like Linux Mint that comes with a lot of libraries installed by default.
Mind that the first time that you use Wine it creates an empty Window$-like environment (PREFIX), just think about a fresh win7 installation, so it may happen that you won't get a software to work by installing it there.
For example if you install a game that requires Physics but the installer doesn't come with it you may encounter problems unless you install the required software in that Wine prefix, the same case happens in Window$ if Physics isn't installed.
Plus beign offline leaves you without the capability to get that software from the internet or to get useful info on how to tweak your game to solve some issues and get the max out of it (again same story when using Window$).
Steam does a great job on a fresh Wine prefix by installing the missing requirements for the game to launch, but sometimes it's not enough and you may need something else (like Physics i.e.)
To easily solve this issue Winetricks is used, it has a list with fonts and libraries and other stuff, once you select what you need it automatically download form the net and install what selected to the selected WINEPREFIX.
I guess you can locally download the "most requested" libraries (such as direcx9, vcrun, etc) to easily access them offline if a game needs a fix.
An alternative is to manually download and install every single library that you may need, but Winetricks is there to do this for you.
Mind that all this downloading and installing libraries has nothing to do with your distro's repository!
That said I strongly recommend to check the
Wine applications database and see what's the dependencies that you may need before going offline.
Would be even better if you install and try the game when online, you can run different installers at the same time, and it's better to have a single WINEPREFIX per game, at least when you try them.
This to prevent that you break a game by installing libraries or tweaking the prefix to get another game on the same prefix to work.
For example, let's suppose that you want to install 3 GOG games, once you downloaded the installers you can launch them at the same time on 3 different prefixes by typing on 3 different terminals (ctrl+alt+t):
WINEARCH=win32 WINEPREFIX=~/.game1 wine ~/Downloads/game1installer.exe
WINEARCH=win32 WINEPREFIX=~/.game3 wine ~/Downloads/game3installer.exe
WINEARCH=win32 WINEPREFIX=~/.game3 wine ~/Downloads/game3installer.exe /nogui
These commands will create 3 different 32bit wineprefixes on your home folder (the . make them hidden) and launch the 3 installers, the /nogui option prevent the GOG installer to crash.
Play on Linux let you do all these operations with a graphical interface, plus it's easier to manage different Wine versions and there are some scripts that install a game and dependencies for you, you just have to point the path to the installer.
Anyway some of these scripts are a bit old and may install and use a very old Wine version, i never used them TBH..
That being said you probably need a newer version of Wine than the one offered by the Ubuntu/Mint repository, they may be a bit old; it's rare that a game that was running on a old Wine doesn't run on a newer version, so you should get the latest version.
I hope this was helpful, if not I or other users are here help out, Wine is one of the best software for Linux and it's getting better and better
You can also check
pcgamingwiki.com, there you will find a lot of tips and every game has link to the Wine app database (see the screenshot)
ps. if you have an AMD card you can boost the performances by using a Gallium Nine patched Wine, you can check the performance difference
on my blog where sometimes I put some screenshots comparing Wine vs Staging vs Gallium Nine