I'd definitely recommend buying a plastic screen to cover it with because they can get easily scratched. They are not that expensive and they're worth having if you're going to take it around everywhere with you.
Plastic screen covers are pretty cheap and they definitely do a great job protecting your screen. If little scratches that you can never get rid of annoy you then I'd recommend getting a screen protector.
I got plastic screen protectors for my DS and they've kept my screen from getting scratched for almost 4 years now.
No screen protectors are just these very thin plastic covers, the touch screen works perfectly through them, I've never had a problem.
You sort of missed my point, what i was trying to say is that if I can touch the screen constantly during gameplay, use the stylus, and draw on it, all without the screen being slightly scratched then putting a protector on the PSP will definitely hold up.
It has nothing to do with the DS folding and the PSP not.