PSP:
On any model, it's ARK-4. Grab your official 6.61 firmware, remove any trace of former CFW, update to OFW, and add your new ARK-4 CFW. It's even updateable right from the console itself. The firmware even allows for WPA2 (something the PSP didn't originally support), which is absolutely nuts.
https://github.com/PSP-Archive/ARK-4 Main link
https://github.com/PSP-Archive/ARK-4/wiki/Recommended-Plugins Recommended Plugins
Vita and PSTV
On the Vita/PSTV side, you still want 3.65 Enso, which you can downgrade to painlessly straight from the browser. Get started with Henkaku in the browser and click Install. Downgrade to 3.65 and make it permanent with Enso. From there, check my older posts about things you definitely need.
https://henkaku.xyz/ Go here in the Vita's browser, or maybe http://deploy.psp2.dev/ or jailbreak.psp2.dev
https://github.com/TheOfficialFloW/enso/releases Latest 3.65 Enso. This is not the old installer or whatever the hell this is.
On the PSP side, you want to use Isage's fork for Adrenaline. Stepping back for a bit, although you can apply ARK-4 to the regular Adrenaline, it's only Isage's fork of it that fixes the PSP's recovery mode's autoboot. And having it autoboot the ARK-4 loader is the preferred way to load ARK-4 now because, as the ARK-4 github states, the Adrenaline Bubbles Manager method installs an older version of Adrenaline.
Continuing, you want to use Game Categories Lite v1.7-js1 by Ticky, making sure to add and enable it in VSH.text and PLUGINS.txt, then going into the XMB Settings (and ARK-4 Plugin Manager) to make sure it's on. This fork is the version recommended by the ARK-4 team (linked above).
https://github.com/isage/Adrenaline/releases/tag/v7.1.7
https://github.com/ticky/game-categories-lite/releases/tag/1.7-js1
https://www.reddit.com/r/VitaPiracy/comments/oygawa/unlocking_ps_vita_1000_internal_memory/ Thoughts on hacking for Vita-1000 internal memory