The PS Vita is a pretty nice system, even if it's losing popularity.
LBP PS Vita is an obvious choice if you like the PS3 one and want to take it on the go.
I would NOT recommend any FPS games for it, despite having 2 sticks since console FPS games are always dirt poor compared to PC ones.
Super Monkey Ball Banana Splitz is pretty same-y compared to recent SMB games and the gimmick of the "level-creating camera" will only keep you playing for so long.
If you like Spelunky, the Vita has a pretty good port of that game for handhelds. (You only get the Vita ports if you want to play a game on the go, but even then, some ports are bad.)
Terraria is a good port of the PS3/360 one, AND you can cross-play online with the PS3 one.
Those are my few bits. Even if I don't mainly use my PS Vita for handheld gaming, it's got the games I want.