Well you kind of answered your own question there.....you say that you want a PSP 3000, which isn't the best model to hack. The easiest to install a Custom Firmware (CFW) on is the PSP 1000 (Phat) whereas arguably the best PSP to have CFW on is the original PSP 2000 (Slim) which came on 3.60. Any PSP 1000 can be "hacked" permanently but only the early to mid released PSP 2000's are similarly vulnerable; the introduction of a new motherboard (the TA-088v3) rendered these latter day slims impossible to install a permanent new firmware on due to a new boot authentication routine (a good guide is those which came on 4.01 firmware and up, although there are countless topics on this board detailing the box info to look out for). The PSP 3000 is similarly unhackable with a permanent CFW.
However, a tiff exploit was discovered in OFW (official firmware) 5.03 which enabled the execution of homebrew on those unhackable Mobo's, and from this a custom firmware was developed to run on them. All of this exploitation was carried out in the PSP RAM though so powering off the PSP lead to it being flushed and the PSP returning to it's "unhacked" state (and as such people use the sleep function rather than a full power off).
Therefore a PSP 2000 with a TA-088v3 or a PSP 3000 can only be "hacked" if the firmware it's running is 5.03 or lower. There is NO WAY to downgrade a firmware on a OFW PSP so if the PSP you happen to get is running a more recent firmware than 5.03 then you're locked out on these PSP's. However, for the PSP 1000's and "hackable" PSP 2000's firmware is irrelevant as a device called a Jigkick Battery allows the PSP to boot from a Memory Stick rather than it's internal firmware...from here the new Custom Firmware can be installed (again, this method is incompatible with the PSP 3000 and latter day Slims....above 5.03 and you're stuck).
So for a PSP 1000 and a "hackable" Slim (see elsewhere on this board for box details) all you need is a Jigkick/Pandora Battery and a special memory stick that you can make to install the CFW (lots of GUI's are available to make these very easily).
For a "unhackable" PSP 2000 and the PSP 3000 you need to be on 5.03 and below, and will then use the homebrew enabler (ChickHEN) to run a temporary Custom Firmware. Note - this appears to be an evolutionary dead end - these PSP's are now out of the loop for the new releases and can't play many of the most recent games requiring the latest firmwares.
That gives you a basic rundown without resorting to another site. Until you decide which PSP you're getting, new or secondhand, then any further detail is liable to be redundant.
(Some of this post may be a bit "mental"...i have a horrible cold at the moment and am using someone else's laptop which is loaded with junk...apologies for any hazy info or stupid errors)
