I highly recommend Killzone if you want a shooter. AC: Liberation is also suprisingly good. The 2 Rayman games and Dragon's Crown are also great.
LittleBigPlanet Vita is a pretty good game. LBP3 for PS4 suffered with connection issues and with generally lackuster new creation tools. That was surprising for me, because it was made by the same studio of LBP Vita. The portable game is a completely different beast: great performance and loading times plus a wide array of touch based creation tools that are actually fun and usefull instead of the PS4 BS they came up with. Also, the Vita version doesn't play the old LBP1/2 levels and the new ones are all Vita-exclusive. So you will actually get access to a lot of levels (and there are really a lot of them) that can't be played on PS3/4.
I would also recommend getting Tearaway. It's maybe the best Vita game. The PS4 version didn't had the rear touchpad functionality and so it is just a pale shadow of the original game.
My last advice is: keep a look at flash sales. I got Hot Shots Golf for 1 dollar, Garou for 3 and so on.
Edit: people already did it, but I have to say it. Persona 4 Golden is mandatory, really amazing game. It actually has new characters and dozens of hours of extra content when compared to the PS2 version. Marie is a new character that has a long, long plot and it's only in the Vita version.
