I think the emulator (versions) you're going to use will be dependent on your PSP type, firmware version, and homebrew enabler option (HEN vs Virtuous Flame, etc.).
The
PSP CFW for Dummies Guide will more or less walk you through which homebrew enabler you want, but I'm not sure how up to date it is and know some of the download links are broken. The
wololo.net homebrew forum is a good place to find working links, newer versions of PSP homebrew software, and discussions of how well which version of which homebrew works on different homebrew enablers. E.g. 'UO gPSP Kai,' a badly named GBA emulator, has newer versions incompatible with TN-HEN, but some not-too-old ones work fine.
Outside of gaming, I really strongly recommend bookr-mod—or bookr, but I've had better luck with the prior—for reading PDFs. It handles image-heavy PDFs pretty badly, but I've gotten a good amount of mileage out of it with novels. bookr-mod lets you adjust how quickly the analog pans the viewing pane and has some sort of faster-but-less-stable rendering mode that has made unusably slow books readable, without too many crashes.
- GBC: I tried using MasterBoy. It seems to run Metroid Fusion/Zero well. Shantae emulated badly on it; tiles were scrambled half the time when exiting the pause menu.
- GBA: UO gPSP Kai played Mother 3 pretty smoothly; haven't tried much else.
- SNES: snes9xtyl. Slightly buggy, requires a little fiddling to break in, and text was kind of ugly in Seiken Densetsu 3.
- Genesis: nfi, sorry.
- N64: No personal experience, but Daedalus seems to be the go-to option.
- PSP: Games are loadable via Prometheus, Aloader, and others. Aloader occasionally will have a rainbow-y border on the edgemost pixels for some games, while Prometheus won't, but Aloader is generally a lot more convenient. I'm sure there're newer loaders out there than what I'm using, too. If you're looking for Japanese RPG-y or anime-y game ISOs, check ffinsider.net/psp-iso. If you're looking for a wider selection of western titles, try devils-shadow.com. (Links are broken due to being uncertain about piracy-linking policy for this board.)
You can try poking around for stuff on
wololo.net's download section, but it's still very beta, so usability isn't really worked out yet, and there's no advanced search. It's sorted by date, though, so it may be a good way to quickly see what's new, with less noise than skimming a PSP homebrew forum.