In My Opinion, so fare most stable Homebrew version of CFW for PSP is
Custom Firmware 3.90 M33-3 which was released by Dark Alex at March 31, 2008.

Here is the most useful links from PSPslimhack

Please select below:

Official Sony Firmware

Custom M33 Firmware (3.90 M33, 4.01 M33 etc)

_HellDashX_ Custom Firmware (3.72 HX)