Same here, my favorite console of all time. Of course modifying a PSVita Slim is super easy nowadays (you literally connect to a site with your Vita and it does everything for you), and when you're done you'll have the best PSP ever. I suggest the Slim model, despite the inferior LCD screen, 'cause in my opinion it's so much better in every aspect that really counts on a handheld - weight, ergonomics, buttons. And the screen is gorgeous anyway.
The PSP library is huge. Lots of tactical RPGs (Disgaea, Jeanne D'Arc), obscure and less obscure visual novels, JRPGs (I've played the first two Trails in the Sky on my PSP, they're still my favorite JRPG), old school platform games... I can't possibly make a list. But I'll recommend a golf game that in my opinion is the best ever, alongside Neo Turf Masters: Pangya.
Pangya was born as a korean online PC game, and it was ported on the Wii, but the PSP version is a different beast. It takes all the best qualities of Everybody's Golf and adds fantasy elements, lots of customizable characters with a long story mode for each one, and tons of items - not just golf equipment, but for example potions that let you cancel the wind, or make a stronger shot. Some of the crazier golf courses have lava, ice, and even windmills where you have to time your shot so it doesn't hit the blades. Just like Neo Turf Masters, it's a game that I can pick up and play even today.
