Welcome to PSPmod
You can buy new, but if you do you will most likely need the game Lumines, or need a Pandoras Battery (universal downgrader/unbricker - modded psp needed to create it)
If you do buy used, lets say ebay try to get a psp with firmware 1.50, the lower the better. Firmware above 2.82 need games to downgrade.
To check firmware from the box
Quote:

no letter = 1.0 (Japanese Release) 1.5 (North-American Release) confirmed
A = 1.5 confirmed
B = 1.51 confirmed
C = 1.52 confirmed
D = 1.52 confirmed
E = 1.52 confirmed
F = 2.0 confirmed
G = 2.01 confirmed
H = 2.50 confirmed
I = 2.60 confirmed
J = 2.70 unconfirmed
K = 2.71 confirmed
L = 2.81 confirmed
M = 3.01 confirmed
N = 3.03 confirmed
O = 3.10 confirmed
P = 3.11 confirmed
Q = 3.30 unconfirmed
R = 3.40 confirmed
S = 3.50 confirmed
T = 3.51 confirmed
|
1.51 -2.81: can be downgraded without games
2.82 - 3.03: needs an unpatched (update 2.00) version of Grand theft auto: liberty city stories
3.10 - 3.50: needs an unpatched (only patched in Japan so far) of Lumines
3.51+ cannot be downgraded without Pandoras battery.