How to go on about modding

I bought a PSP a while back that came pre-loaded with a bunch of games, so I'm pretty sure it's already modded. However, the memory card is completely full, and it’s acting up to the point where I can’t actually play anything.

Since this is my first time ever owning a PSP, I’m a total beginner. Can I factory reset the console to wipe it clean and then mod it properly myself? Also, what is currently the best, most reliable software to use for modding it? I'd love to get it working so I can use it for games, music, and videos.