I have firmware 3.60; what Homebrew and etc can I do with it

welll to be able to run homebrew u need a CFW(custom firmware) try gooogling 3.60 to ___ (what ever firmware u want)
(google and psp fit hand in hand)............u might need a unpatched copy of GTA Liberty city stories

[ace]

You can use a pandora's battery to upgrade your psp to any custom firmware now. Once you have upgraded your psp to a custom firmware then you can run close to any homebrew you want to, emulators or whatever.

Theres plenty of tutorials in the tutorials section, so you can try out dpm's tutorial on making and using a pandora's battery.