Definitely try and get a Core PSP-2000 now. Those are the PSP-2000, the slim type. The ones that are package with Ratchet and Clank are the ones that are PSP-3000. They have the brighter screen but have some screening problems as was presented over the internet.
Games, I would get:
Metal Gear Solid: Portable OpsGod of War: Chains of Olympus
Tekken: Dark Resurrection
Those are some good games that will have your PSP running :)