I know this is probably a loaded question but I want to make an informed decision before I buy one.

In terms of speed, all PSPs use the same processor and almost all of them have the same RAM amount. (The PSP 1000 is the only one with 32 MB of RAM and system storage while the rest have 64 MB RAM.)

However, only the PSP 2000 and the 3000 have Video-Out capabilities, making for easier screencapture. Aside from physically different sizes (2000 has a bit of thickness to it), the only two differences in their hardware is that the 3000 has a built-in microphone and starts on a higher version of system software. (The component cable needed to use this function is also in the article below.)

Scroll down a bit from here for the table of specifications: https://en.wikipedia.org/wiki/PlayStation_Portable#Designs

Be really careful with sellers of these. There's a lot of "for scrap only" on the market, (as in, only a few parts are useful,) as well as a whole lot of people selling who don't list the correct model type. It's been a month or two since I've been watching, so there may be some good stuff out there.