You should get at least a 1 GB stick, they are cheap now and you will fill it up in no time. As for games, can really only coment on the ones I own, but..
Twisted Metal: Head On
If you are a fan of TM you will love this, it kinda takes place after TM:2, bring back some of the only char's picking up on their old plots. Really fun game that you can play on the go for short bursts.
Monsters Hunter Freedom
I loved the first MH on the PS2 and this one is just as good. It takes a little while to start getting the better gear and killing off the bigger monsters. Might not be a game for you if you are not into very heavy crafting and farming.
Valkyrie Profile: Lenneth
If you already own the PS1 version, there is a lot this one if going to offer you, though if you don't I would say go ahead and pick this one up. Fun, though short little rpg.
Metal Gear: Acid 1/2
Seems these are love or hate. I found them to be okay, but no big deal. You can get both of them pretty cheap now though. For me nothing really stood out to make ether game great, but then again I am not a big fan like some.
Armored Core: Formula Front
If you are a AC, this is a no brainer. Great game, controlls hold up well on the psp, and it looks pretty good. I really didn't have high hopes for this one but it turned out really good.
Tekken: Dark Resurrection
This game is aswome, I always have been a 2d fighting fan, so never really big in Tekken, but this one is really fun. Much better than Darkstalkers( though a good game ) and Streetfighter for the system.
There are a couple others that are okay. Not sure what you are intrested in so eh. Also if you are into importing there are a ton of good games that have not / will not be coming to the states.