I'll try to withdraw as much of the quality judgement comments I can, because they will just invite an edition war, and those guys in the edition wars are...less than nice to even consider.
You have the most recent editions to look towards. The old ones still exist and are still played, but you'll find more players for the newer ones, so I just recommend pickiing one of them. I'll try to list some advantages, but it's mostly a matter of personal preference.
Edition 3.5 (3.5e) - there was a 3rd edition but the rules got amended into what became 3.5. It's probably the most well known edition, rules-wise, if you've played Neverwinter Nights, KotOR or other more recent games based on D&D (Planescape and Baldur's Gate are based on a previous edition). An advantage would be that the bulk of the rules are free and over here [http://www.d20srd.org/]. I haven't actually went through to see how good they are laid out, though, but it should have everything you need to play - races, classes, skills, spells, etc. Also, the edition ended and is discontinued...so take that as you will.
Fourth edition (4E) is the current one. Sort of. It's being wrapped up and finished soon, though. Doesn't have free stuff, however, since it's finishing, you can most probably find the core books (and probably other 4E books) for cheap, so a plus, side I guess. You'll need the Player's Handbook (PHB), Dungeon Master's Guide (DMG), and Monster Manual (MM) at minimum to play. I think they also have "starter pack" or something similar with those three books included. And another note, PHB2 and PHB3 add more races and classes, so you might want to take a look and see if you want them, too. There is a DMG2, but I don't know whether to recommend it or not. I believe, it's an addition to the other one, not a replacement. And there are MM2 and MM3 for even more monsters, but if you're buying the books one by one, I've heard Monster Vault is actually better to get instead of MM. I hope that wasn't too confusing, since I just gave you lots of names. Also, 4E is more friendly towards new players and, for better or worse, easier to play over the internet.
Pathfinder, also unofficially called 3.75 edition (as in, halfway between 3.5 and 4E) is mostly 3.5 with rules tweaks and additions. In fact, often people talk about 3.X edition, which is 3e, 3.5e and PF. And it's still running, so there is that. PF, has the bulk of the rules for free [http://www.d20pfsrd.com/], too, just like 3.5, which is a bonus. And finally, it boasts full compatibility with other 3.5 products but the extent of that is a little debatable.
So, in short, 3E is easier to start off in, while 3.5e/Pathfinder are free. Take your pick. It's probably easier to find a group and play whatever they are playing, though.
