If you plan on replacing the firmware then the 1000 is the only one that works 100%. The 2000 models depend on the board version inside and it can be hard to tell.
My 1000 is already running custom firmware. I'll probably keep the new one updated through Sony since I don't really need 2 softmodded psps.
Actually the newest
PRO custom firmware can run on any PSP model, even the 3000 and GO, and actually runs on top of the latest 6.60 official firmware. Your PSP boots into the official firmware first and then you run a program from the game menu to boot into the custom firmware. It stays on the CFW until you reset your PSP.
I've been running it for about a week and everything seems to work fine, all my emulators and game backups run great.
As for which one to buy I've owned both the 1000 and the 2000 and the 2000, in my opinion, is much better. It's smaller, much lighter, and has a better screen. While I haven't owned a 3000 I have played one and at least the early models had pretty noticeable ghosting when stuff moved around on screen.