It depends on what firmware the PSP you get is running.
The only real issue is that if you get one with firmware 2.81 or above, you will need a copy of the original issue, unpatched version of Grand Theft Auto: Liberty City Stories (the one with the firmware 2.0 update on the disc) in order to downgrade.
Downgrading to an earlier version of the system software (firmware) is the only way to get access to homebrew on your PSP (sony have patched the parts of the firmware that hackers used to get access in newer firmwares).
The only way to downgrade a psp that has firmware 2.81-3.03 requires a copy of that game. This is the only 'hole' hackers have found in these more recent firmwares.
Homebrew is downloaded from the net with your PC and then copied over to your PSP (saved onto the memory stick). I would recommend at least a 1GB memory stick (I have a 4GB, they get quite expensive though).
You will also need a USB cable to connect the PSP to your PC, or if you have a card reader that supports memory stick pro duo cards you could use that to copy things over.
I could give you links to guides on downgrading (most of ours are by evolve) but which one to use depends on what firmware your PSP comes with.
As soon as you get the PSP let us know and myself or one of the other forum members will help you get it downgraded.
Welcome to the site BTW.