Inherited a PSP - what to do with it??

So, as the post says, I recently inherited a PSP from someone and want to know what I can do to get the best of it.
I'm fairly sure it's a PSP-2000, but only because of the location of the 'Sony' logo on the front top-right, but I do know it's got v4.05 firmware and isn't hacked. It also came with a 2GB memory stick.

I have a PS3 and am looking forward to playing the PSN+ PSOne freebies on the PSP, but I'd also want to play a few of my actual PSOne games on it without putting down close to £10 for a 15 year-old game. Is it possible to import them or are the PSN releases actually 'updated'?

I'd also really like to use emulators for SNES\Mega Drive (Genesis) games - is this possible to do legit, or is this a custom firmware-only option?
If it can only be done with custom firmware - what are the problems of linking a hacked PSP with a legit PS3?

I'll add more as I think of it :-D

EDIT: MOAR!!

So, I've found out I can re-download my PSN-purchased PSOne games, is there a way to transfer them directly from the PS3? Redownloading them all one-by-one is a PITA...