I've moved your thread into the correct forum for discussing mobile gaming.
Welcome to the forum BTW.
Now to your question. As your PSP is already using a custom firmware you don't have any issues to worry about. You can simply upgrade it directly to a newer custom firmware.
If you are not looking to play anything that needs the 3.60 or newer firmwares then I would recommend you stick with the slightly older but very stable 3.52 M33-4 custom firmware. A big advantage of sticking with 3.52 is that is still includes direct 1.5 kernel support for 100% compatibility with older games, as well as emulators and homebrew games and utilities.
However, if you really do need a newer version then you have a few to choose from with the latest being 3.90 M33-2. But you will first need to upgrade you PSP to the 3.52 M33-4 custom firmware before you can then install any of these newer ones, so I would recommed upgrading to 3.51 M33-4 and using that until you find you definitely need a newer version.
For installing 3.52 M33-4 read my original post
here on how to install 3.51 M33 as it is basically the same process for 3.52 M33. And to download all the files you will need go
here.
And also have a look at this post on another forum
here. This outlines all of the steps needed to upgrade from your current firmware to either 3.52 M33, or all the way up to 3.90 M33 v2.