PSP Vita question

Been thinking for a while to get a psp vita and have not really looked too much into what games are great or not, so i was wondering what some good games are to get for it? so far on my list i have:
Persona 4 Golden (since my ps2 version does not work anymore ><)
Disgaea 3: Absence of Detention
Metal Gear Solid HD Collection
and was wondering if Persona 3 for the psp would work on the vita since a friend of mine was aying some of the psp games do work on vita

most psp games will work on the vita, but check the psn store first as they will Most likely state on the game page if the game will work on the vita

The only psp games that run on vita are the digital copies off psn so check first if the game is in the store.

All my PSP are on my Vita... eCfw is the way. And no I didn't pay nor psn download.

If you're into shooters, then Killzone: Mercenary is a decent game. (aka the only good shooter for the Vita, at the moment)

And a few other possibilities:

Lumines: Electronic Symphony
Gravity Rush