I'm bored, so fuck it, I'll try and list some good shit to have when you CFW.
For CFW, there's a shit ton of different versions, but currently the best one would be ME. Shit's recently updated to incorperate the Pro C online shit as well, so you can connect Ad-Hoc games to a server to play shit online still such as MGSPO+, MHP3rd, etc. Link has the shit needed.
Of course 6.60 firmware needs to be installed before you bother, and depending on model/motherboard of PSP if you can perma or have to always refresh upon cold boot.
wololo.net/2014/12/14/psp-revision-2-310-3-of-the-me-lme-cfw-is-now-available-adds-pro-online-support-dax-format-and-more/
Next link is to do with the online shit and how to set it up. Plugins are easy as fuck to set up, make a folder on the root of your PSP memory card named seplugins and drop shit in there. It's a little more complicated than that, but not by much, I'll follow this with a guide. 2nd link is the server status of Coldbird, which is the server for all this type of shit.
forum.coldbird.net/viewtopic.php?f=2&t=14
pro.coldbird.net/status/status.xml
Here's a guide to plugins. Simple shit, and it'll become second nature after a while
forums.afterdawn.com/threads/guide-how-to-install-plugins-on-a-psp-includes-on-how-to-install-two-or-more.657638/
You this far? Good. Here's some more good shit. POPSloader is the built in PS1 emu used for Eboots. Once this is set up, all you have to do is download eboots (ISOZone and Emuparadise are good for this shit) and put them in PSP/GAME/Foldername and they'll appear. Note that folder names can't be too long or they'll appear as corrupted. 2nd link is another download of POPSloader for 6.60.
nicoblog.org/psp/how-to-use-popsloader-guide/
theisozone.com/downloads/playstation/other/popsloader-v3-for-660-pro-cfw/
That's the main shit all set up of your PSP if you've read this fucking far. Next up, emulators. Shit's generally easy to set up since it's usually drag and drop, and some emulators require bios files to work (Sega CD region BIOS, GBA BIOS, all are on Emuparadise when needed). Outside that, just do the same as you would any emu, set up, download ROMS (or a fullset if got the space) and play.
wiki.gbatemp.net/wiki/Emulation_on_PSP
Need some apps or extra homebrew shit? PSP has that going for it as well. Model 1000 can utilize the IR sensor on top to turn into a universal remote, can get a homebrew Ebook reader, a port of DOOM/Cavestory/Quake, or even completely new games like a Touhou created for PSP. Also apps like PSPFiler for exploring your system if you can't be fucked to connect to a computer, or PMPAdvance for a better media player. Links are to some sites that are good for exploring for shit. If you want a basis of what to look for, check Wololo's homebrew top 50 charts for the years and see what appeals. Oh, and CWCheat if you want to cheat in shit (or sometimes needed to get more out of a game, like Monster Rancher for PS1).
wololo.net/downloads/index.php/download/479
psp.brewology.com/downloads/
Last but not least, PSP games. You know what you want to play, shit's easy to download (Emuparadise), get to it. Maybe invest in a memory card adapter so you can have a ton of shit on your PSP with the use of 2 micro SDs. I run 128GB myself, but probably can go right to 256gb if you give a shit enough.
Last note, PSP has a lot of translations and mods for games as well. Nicoblog usually hosts the weirder shit (Project Diva with translation patch/plugin, Valkyrie Hearts 3 Extra Edition, etc) as well as the more 'harder' to get games (Corpse Party). If it's not on Emu, try Nico, they'd usually have it. If they don't, fuck knows, explore.