I have a 1000, 2000, and 3000. I also have a DS. Personally, I would choose the psp, because when homebrewed, it can do maaaaannnyy things.
If you get a psp, do not get a 3000. You can homebrew them, but temporarily. You have to re-flash the bios every time you use it.
I prefer the 1000s and the 2000s. The 1000s have the infra-red on them so you can use them to turn on TVs etc. etc. and are by far, the easiest the hack. The 2000s are pretty much the same thing, but are slim, light, and have the mic in the corner. You can also download a pop-up app to increase the back lights brightness which surpasses the 3000s.
Homebrewing your PSP enables you to run emulators such as gameboy, SNES, n64, etc. consoles. It enables you to download PSP games on the internet, and put them on your psp and play them, WITHOUT having to buy them.
There are tons of things you can do with them, you just have to know WHAT you are doing.
Recommended though, if you are looking for a psp 1000 or 2000, do not buy one that is updated past 5.03 official firmware.