For those who prefer to use separate folders to separate their fighting games from puzzle games, or their RPGs from platformers, there is only one firmware option:
5.00m33-6
For this you will need the Game Categories plugin and a hackable PSP.
Sony gimped the 6.xx series firmware by reducing the total characters that can be used for directory structure and also removed the charming background preview images that are used for both PSP and PS1 games. With 6.xx, you'll find that you run out of characters to properly name all of your folders.
Using category folders is recommended for emulators too, but on the PSP it has the added benefit of speeding up the process of finding the game you want to play. That's due to the fact that the PSP's interface is laggy and doesn't automatically highlight the last game played.
When setup properly, there's no notable compatibility difference between 5.00 and 6.xx.