I'd like to play some Unreal, but I really don't want to spend all the money on all of the games. Which one is the "best one?" I'll probably end up getting the rest later.

I personally fancy the first, Unreal Tournament 99 and preferably GOTY(game of the year) Edition but I'm a bit biased :) . On the other hand 2004 is also very good and worth playing.

Yeah, i like UT:GOTY the best, too, and then Unreal.

All are good, but Unreal 1 is my favourite.

This is a hard question to answer.
Unreal and Unreal II are single-player affairs, while UT and UT2k4 are exclusively multiplayer (yeah I know you can play SP with these, too, but it's blah).
So, if you fancy the story-driven kind of linear single-player experience, I'd say go for Unreal Gold. If you're feeling deathmatchy and capturetheflaggy then go for UT2k4 IMO.
You'll have buckets of fun either way, though.
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Unreal 1 is my favourite too, by far.

Thanks for the advice, everyone. I'll look into your recommendations.

What many others have said I'll add to. Unreal 99 GOTY has many many maps and modes but 2004 added vehicles and a few other modes along with updated graphics. In my opinion the order goes 2004, GOTY, Unreal and Unreal 2. The single play experience in the Unreal series is pretty good, but I've found I like the multiplayer setting of Tournament a lot better and 2004 added a lot of elements with vehicles and such.

I don't think I'll add something new, but anyway I'll give my opinion as well.
Unreal 1 if you seek an unique single player experience, with beautifully designed maps and music, and UT2004 if you seek a big re-playability (tons of mods, I made a topic about this) and good multiplayer.

You could always try the UT2004 demo making a choice. http://www.gamershell.com/download_5054.shtml

For single player, I'd say play Unreal 1 in Unreal Tournament using the OldSkool Amp'd mod, and the S3TC hi-res textures.
If you like playing multiplayer objectives based fragfests that have map bottlenecks with human team against bot team and/or have some pretty old computers with weak graphics cards, I say go with UT99. Make sure to try out assault map AS-Overlord. (UT GOTY).
If you want better graphics, and/or vehicles and better internet play, I say go with UT2004, thousands are still online playing it. Onslaught was the big mode in this game, the demo allows you to try out the Torlan map. There is a surprising amount of strategy in this mode if you give careful thought to weapons use and vehicle strengths and vulnerabilities.

I don't know that this is a better vs worse thing. They are distinctly different games imho.

Ut99 is smaller, faster and simpler in most ways. It has a ton ton of stuff like ctf stormchasers and other whimsical maps that simply don't get remade in later editions. Assault in ut99 is an entirely different experience than 2k4. People are still modding and mapping for this game. It is my wifes singular favorite game, and she entered gaming via borderlands 2. That says I ton about the game, since it competes with games made much much later on.

ut2k4 saw some drastic changes, and is awesome in it's own right. Vehicles, adrenaline , zoom instagib and so on. A little bigger, and slower than 99. Probably more/better mod content. Much better visually.

Unreal 1 and 2 are fun single player, unreal 1 is among the best deathmatch one can play. Also, getting good at these games will improve your fps skill in general.

Honestly, I would say buy the pack. Play unreal 1, all the way through, then ut99, then 2k4. Once you're hooked check out ut2. it is the glitch filled stepchild of better software, yet is a single player masterpiece of it's own.

2k3 is another story. The weapons are a bit different, which is huge.

Oldskool is a very old SP emulation mod for UT which uses a much older version than the latest version of Unreal Gold, there's not really any point in playing Unreal or any of it's older mappacks within oldskool when you can play them straight through the latest version of Unreal.

Then there's also various maps that have been made with the latest version of Unreal (227i is the most recent public version, but 227j is in the final polishing stages before being released at the moment), which would just not run at all in UT (which use features and the new engine updates from 227i/227j).

I know there are some other mappacks which were made with UT in mind, but those mappacks such as ONP, Xidia, 7bullets and Zephon can all be played from Unreal Gold by using the latest version (you also need a mod, but I'm not sure what mod is required to run them. I just know that I played them some years ago on Co-op over Unreal Gold but I didn't think to ask how they were hosted. Possibly the server was using XCoop.)