Lets be straight and short.
If you want the games you can find on the shelves for free.. i cant help you in that part because its ilegal.
If you want homebrew games ( this means games coded by other people ) your PSP must be 1.5 or 2.0 ( 1.5 ensures total compatibility ) you can also downgrade it from 2.0 to 1.5 which is easy.
As any homebrew ( as ANYTHING )
you download from the internet you should download it from sites you trust ( pspupdates is trustable ) and to be even more sure you can download a program that checks a certain homebrew if it has suspicious access to the place where firmware is installed on your PSP ( a chip ).
Before downgrading you should be careful and double check every step you find in the readme.
I wasnt that short was i?
Anyway lets resume things:
Pirated games -> Cant help
Free games -> Homebrew -> 1.5 or 2.0