depends on how far you want to go
TN-E HEN is the easiest. You can play ripped/downloaded games, apps and a few other tasks by dragging two files onto the memory stick. It works with every model (1000 to 3000 and Go). On the PSP, just activate the TN-E HEN, which allows for unsigned apps to run, and from there you can run emulators or iso loaders or whatever.
Full CFW stuff, which I personally don't bother with anymore, is supposed to be better and that works with the 1000 and 2000. I don't know if it's on the 3000 or Go yet.
For the hardware, I think the only two sold as 'new' are the 3000 and Go. Don't know what the MSRP is these days, but I got my Go for $100 a while back and it was totally worth it. I play my PSP games on that (have to use my old 2000 to rip UMDs still). But the Go has a smaller (but best of the bunch) screen, is less comfortable to play for extended hours, worse battery life, requires more proprietary shit, non-removable battery, etc. I use it because, well, I really like the Gameboy Micro too, so it's a theme.
also, at least on the Go with TN-E HEN, 100% of games don't run perfect. Most of the popular ones seem to be fine, but like Mega Man Powered Up had crackling sound occasionally.
to briefly get into the minor differences between the 2000 and 3000: the screen on the 2000 has bad ghosting. 3000 fixes this, but it can have interlacing-like small lines on the image). Go has the best PSP screen, even at the smaller size (I think it's 3.5 or .7 inch compared to PSP 4.3).