There are indeed plenty of PSP games to own such as Daxter and God of War : Chains of Olympus.
I'm not so sure about your left hand...if you can still play games fine with Xbox360's or PS3's controller then u should be fine somehow with the PSP...however u could get those hand grips strap on for better comfortably of your hands on the PSP...kind of like the PS3 controller in a way.
I enjoy using my PSP mostly for trips/vacations even I get to transfer PSone games from my PS3 to my PSP on the go...I could also transfer some movies (althou its a real pity that almost all movies dont have english subtitles on the PSN video store) to the PSP as well.
I use the 4GB memory stick which is good, but I might eventually need to get an 16GB or even 32GB memory stick for a WHOLE LOT of data to be held on my PSP lol.
PSP is usually perfect for playing games on the go so...its a great system, with lots of games to play and some good movies on UMD to watch, but what really sucks is the battery life as it is often needed to recharge alot.