3.40 OE-A firmware but i need 6.20; What update should i get?

It has been a few years since I've touched my PSP and I've given it to my nephew recently. He bought a game that requires 6.20 firmware and I don't know what new custom firmwares are our and compatible with what.

I know there's probably a list somewhere, but can someone tell me which is the best/safest to use? I haven't messed with homebrew in years and now i'm confused by it all.

I'd appreciate any help. Thanks :))

if you want to stay on custom firmware then you'll need 5.50 GEN

Is it possible to just do a sony update to 6.20?

Sorry but you didn't help at all. It told me i couldn't use GEN D or whatever when i tried updating it.

I just want to do a regular sony update from the custom firmware i have so i can give my psp away.