My PS2 games look even better on the PS3. Now, I'm not sure that every old game will play on the PS3-it may be like the XBOX 360 where certain XBOX games didn't work. I have both
Lego Star Wars, Kingdom Hearts I and II and God of War and they all work great on the new system.
You can save to the hard drive, but you can also get a card to move your saves from your PS2 over to the hard drive, so if you don't want to lose your place in a game you don't have to.