Best vita/psp/psx games for someone who's never owned a PlayStation before?

I got myself a 2000 model Vita from Japan last summer, it looks great but I haven't had much time to play on it yet. I've never owned any Sony consoles before and spent most of my childhood playing on Nintendo systems and on PC, so I'm looking forward to getting into the best stuff I've missed out on from the past few decades.

I've heard that the Vita is mostly good for playing RPGs and indie games but I'm also interested in anything you can recommend in any genre - remastered classic PS games, PSP/PSX games through Adrenaline, homebrew Vita ports, etc. What's the best the Vita has to offer?