I think there are way too many menus on my PSP that I will never use, like the Extras Menu, Videos and Music etc. Is there a way to remove those without resorting to a custom firmware?
If not, is there custom firmware that allows that while still being able to play my legally owned games?
It cannot be done in the original firmware. You'll need custom firmware for this.
The good news is, custom firmware these days is dead easy to install: update the PSP to the latest official version, drag and drop the installer onto the PSP, and run it. It also doesn't interfere with legally acquired games - you just put the game in the drive and play normally. And if it does turn out to interfere with one of your games, the most popular custom firmware, PRO CFW version C2, boots into the plain Sony firmware and needs to explicitly activated afterwards - so if you're having problems, just reboot the PSP and you're running the plain firmware again.
Once you have custom firmware installed, plugins like XMB Item Hider can be used to customize the main menu.
