My favorite main-stream games, and therefore most likely inexpensive, were God of War 1&2, Devil May Cry 1&3, Kindom Hearts 1&2, Final Fantasy X, Shadow of the Colossus, and Silent Hill 2. There are lots of great non-mainstream games, like the persona and disgaea series, and Ico, but those games might be harder to find, and they'll probably be a lot more expensive than the other games I listed.
I would recommend buying a genuine Sony memory card because the non-genuine cards are more prone to failing.
If you're buying new, you can only choose the slim, but if you're buying refurb or used, I'd recommend a slim. The phats had a higher failure rate than the slim, and the slim uses less power and takes up a lot less space.
I had a phat that I purchased a year after launch, and it lasted me 6 years before I knocked it off a dresser and onto a hardwood floor. If you treat it well, it'll last a long time. There was a lot less technology in the PS2s than current gen systems, and the parts were so small and power-efficient in the slims, that they have a very small failure rate.
The component cable that was recommended will only help with games that support progressive scan, of which, there were a few. If you buy it from monoprice.com, you could pick it up for under $10 shipped.
