Which PSP you need?
There are currently two quite different PSP models available on the
retail market (PSP-3000 and PSPgo), or three if you look carefully
(PSP-2000), plus another you can find used (PSP-1000). That makes four
PSPs to choose from, and though three of those models are quite similar,
each one is a little better for a different specific use.
The Best PSP for Homebrew: PSP-1000
The first thing to consider when buying a PSP is if the machine will be used to run homebrew
programming, or if it will simply be used for games and movies
available in retail shops or from the PlayStation Network. Most buyers
are unlikely to run homebrew, as it takes considerably more work than
retail games, and it requires some knowledge of programming.
The Best PSP for UMD Gaming and Movies: PSP-2000
If you're just looking for a machine to play retail games and movies or
PlayStation Network content, then the PSP-2000 or PSP-3000 will be your
best bet. The main difference between the two models is the screen. The
PSP-3000 has a brighter screen, but some users saw scan lines when
playing certain games. Most players probably wouldn't even notice, but
if you're picky about graphics, then stick with the PSP-2000.
The Best PSP for Portable Gaming and Movies: PSPgo
If you're excited about downloading games and movies, and don't care if you ever see a UMD
game or movie again, you might consider the PSPgo. It's definitely
smaller than the previous PSP models, being a size that you could
actually carry in a normal-sized pocket.
The Best PSP for All-Around Performance and Value: PSP-3000
I suspect most users are going to want the best value for their dollar,
which I think you'll find in the PSP-3000. It's not as small (and thus
not as portable) as the PSPgo, and it doesn't have any internal memory,
but it does have a UMD drive, and memory sticks don't take up much room
in your pocket (and with the right memory stick, you might not even need
more than the one in the memory stick slot of the PSP).