All 3 models are very similar - from a functionality standpoint they're the same, they all do the same things, play the same games, same features, etc.
The 1000 is no longer made so you can't get it new, it's also heavier than the newer ones. It also has less onboard storage than the 2000 & 3000. I'd rule this model out. The only feature it had that the newer ones don't is an infra-red (IRDA) port, but that wasn't used for much.
The 2000 is lighter, some of them have had dead pixels. It's no longer made but can still be purchased new.
The 3000 is about the same as the 2000, but has fewer dead pixels - instead it has scanline issues. The screen is brigher too. Both the 2000 & 3000 have double the onboard memory of the 1000. You can read about the differences in more detail here; http://en.wikipedia.org/wiki/PlayStation_Portable
Then there's the recently released PSP Go - it's got a different form factor (smaller, with a slide-out screen), adds bluetooth costs $80 more, has a lot more onboard memory but does away with the UMD drive, so you've got to download all the games.
I'd go with either the 2000 or 3000 so you have the option of buying used games or renting them. Either the 2000 or 3000 should be fine, the 2000 might not be available new too much longer though. Eventually Sony may phase out the 3000 in favor of the Go as well, they claim that the Go isn't a replacement and both models will continue to be sold but video game companies always say that - even Nintendo did with the NES when the SNES came out.