As long as you are buying the "newer" slim models, you should be okay. It's first generation Sony systems that tend to have hiccups. My first PS2's laser stopped working a few years (like 3 years) after I got it, my PS3's PS1/2 reader doesn't work properly, and I haven't had much issues with my PSP since its the new slim model, but the first generation models were notorious for pixel screen deaths...

Yeah, go with the PS2. I do like my PSP but considering the majority of games I've bought for it are ports and remakes of games I own on console, I can't recommend it's library when compared to the PS2 which has quite possibly the most well rounded and solid library for a console.