Are we talking a PSP or PSP Slim?

I've done it with both, but a PSP Slim requires a PSP because it cannot "pandorize" a battery (Sony removed its possibility from new PSP Slims). Although you can try to "hard-mod" the battery, but I don't recommend it.

This link will help you create a magic memory stick GUIDE: Universal Unbricker V3 Using Official Firmware FAT/SLIM PSP. .

I'm afraid about how far I can go about ROMs, so I won't touch that, but I recommend at least 3.71 m33 CFW.

You can also rip your PlayStation games to put them onto your PSP. And it's strange becuase a PSP can barely emulate an SNES, but PSX games run almost perfectly.

Don't hesitate to PM me for more info.