Full disclaimer - I have never owned a Vita but did consider owning one at one point. I have however owned every model of PSP at some point (apart from the cheap neutered final release, the E1000) and played a fair few games.
Personally I'd go for the PSP 2000 or 3000. The screens are slightly different, and the 3000 has a built in microphone, but they're near enough identical. The 1000 has a little less RAM, which makes a moderate impact on loading time, but it feels really sturdy compared to the toy like plasticky later models.
The PSP has a far superior game library than the Vita, and whilst you can play PSP games on the Vita it's far cheaper to buy second hand games for the PSP as opposed to getting PSP games from the PSN for the Vita. If you're a fan of RPG's or SRPG's the PSP is a dream console for you. Furthermore, the PSP is also a stellar emulator. Make a list of the top Vita games and the top PSP games and then consider what suits you better. The PSP has some games exclusive to it that are really worth a shot (Jeanne D'Arc, Z.H.P. Unlosing Ranger VS Darkdeath Evilman, Secret Agent Clank, Final Fantasy Crisis Core, Kingdom Hearts Birth By Sleep, Castlevania The Dracula X Chronicles) and a boat load of non exclusive but still exellent titles (the God Of War games, Valkyrie Profile, Valkyria Chronicles 2, Ys Oath of Felghana, GTA Liberty City Stories and Vice City Stories, Tactics Ogre, Daxter, Patapon 3, Persona 3 Portable) etc etc etc....then throw in all the PSX games you can get on the thing and it's an awesome and cheap travel companion.
If you don't mind slightly older games then get yourself a PSP and a DS Lite and you're set for a long time. The Vita just doesn't have the breadth of titles in my own personal opinion.