Most things come down to opinion, but I'll tell you what I think.
2000 has the best music and backgrounds of the 3. If that's all you were looking for, you'd be set with this one. It has a lot of effort put into it, because I think SNK knew it would be their last KOF. That's why (I think) they threw in all the extra strikers (not to mention they seemed to wrap the story just in case there wasn't going to be a KOF '01). It's got strikers from a lot of other Neo games like Samurai Shodown (Nakoruru), Last Blade (Kaede), Metal Slug (Fio), and even that robot guy from Robo Army.
Unfortunately 2000 isn't as fun to play as '01 or '02, in my opinion.
'01 and '02 are both a lot of fun for me but because they play a bit differently, they're kind of hard to compare. '01 has a lot of crazy combos involving strikers that can end a round real quick. It also has wire damage which equals free DMs for a number of the characters. Some people complain about '02's BC combos. But to be honest, I'm not really good enough to take advantage of them (the damage is scaled down, so you really have to be good to make it worth your while). On the other hand, I can abuse the hell out of wire damage.
For me, '02 edges out '01 because of the roster. '02 is the only KOF with the New Face/Orochi team, and Billy, Angel, and Ramon and Vanessa all in the same game. I wouldn't say it's a cut and dry choice, though. There are people who's opinions I respect who prefer each. The best idea is to put some time in on each and see which style of play you enjoy most.
I went through the exact same choice a couple months ago. I tried them all, and weighed all their strengths (and I could only afford one). There were parts I liked of each, but in the end, I bought '02.