Here's the rundown on PSP models:
- All of them can be hacked on any firmware. 6.20 and 6.60 are the preferred firmware numbers, but 6.61 is perfectly usable. Downgrading is super easy too if you want to go down to 6.20 like I did.
- PSP 1000 has less ram than its counterparts, but that largely only matters for a couple of emulators. Otherwise it's fatter,, the screen isn't as bright, and you would probably have a hard time finding one in great condition at this point unless you prowled somewhere like Ebay and paid too much for what is the most inferior PSP model.
- PSP 2000 and 3000 are essentially identical, although many prefer the 2000 as the display is arguably better. There are reports of visible scan lines on the 3000 model that really bother some people, and I've even seen some ghosting. These issues are pretty minor, but they are enough to drive some people away from the 3000. As well, there have been plenty of reports of the PSP 3000 having this weird white outline issue with perfectly rounded corners on the screen. It is fairly translucent on most colors, so once again, it's a minimal issue, and I'd say only about 15% of 3k models ever had the issue, but depending on how picky you are, you may want to actually see the display in action before picking up a particular 3k model.
- PSP Go is the smallest and most compact of the PSP line and is fairly convenient for its slide out design that minimizes how wide the system is while maintaining the same screen size. The 16GB of built in storage is pretty nice as well, as you really don't need more than that unless you can't make do with 10+ PSP games or any other division of content you can think of at one time. There are two potential caveats though: the size can be difficult to manage for those with larger hands (the button layout is only the width of the screen), and there is no UMD slot for those interested in actually using physical games.
The 2000 and 3000 are the easiest to find, so you're probably best off picking up whichever one of those is easiest to get your hands on. If you can find a reasonably priced Go, after using mine quite a bit already, it's an easy version of the system for me to suggest.
Other than that, any PSP model, any firmware, you're good. Installing CFW is as easy as copying some signed files to your PSP and simply running them from your games menu. It is a pretty much idiot proof process, so even someone completely new to the scene runs near zero risk of even sort of bricking their PSP.