PSP Firmware 3.90: Compatible With All Models?

Yes. PSP Firmware 3.90 (released Dec 2007) installs on every PSP model:

• PSP-1000 (Fat)
• PSP-2000 (Slim & Light)
• PSP-3000 (Brite)
• PSP-N1000 (Go)
• PSP-E1000 (Street) (shipped with 4.00+ but can downgrade to 3.90 if motherboard TA-088v3 or earlier)

Model-Specific Notes

• PSP-1000/2000 (TA-085v1/v2): Fully hackable (Pandora Battery + Magic Memory Stick) on any firmware including 3.90.
• PSP-2000 (TA-088v3) / PSP-3000 / Go / Street: "Unhackable" on OFW 3.90+. Require 6.61 PRO-C2 / Infinity CFW (works on all models, all OFW up to 6.61).
• Features in 3.90: Skype (Slim/Go only), RSS Channel improvements, PlayStation Network sign-in stability.

Recommendation

Update to 6.61 OFW → Install PRO-C2 FastRecovery (temporary) or Infinity (permanent on 1000/early 2000). Best homebrew/plugin support, plays all PS1/PSP ISOs, runs CWCheat. No reason to stay on 3.90.