I haven't actually used my PSP in over a year.. but everything was pretty easy at the time. There are PS1 games that won't work, of course, but I think many do, and they work quite well. It's Sony's emulator, IIRC. I've only played Gran Turismo and FF7, both worked perfectly.
I didn't do much Web stuff because the browser was brand new at the time, but text entry wasn't so easy. It's amusing for "warwalking" though
I highly recommend Squarez. I spent more time playing that than doing anything else with my PSP.