I have an ASUS M3A motherboard, which Driver Manager identifies as an AM2/AM2+/AM3 M3A79-T Deluxe MB.
What is the fastest CPU I can safely/easily install? Or will I have to update the BIOS as well?
You can go with a quad core 9750 or faster dual core, such as the 7850. The board won't work with am3 or phenom II cpus. I would flash the bios first with your older cpu; use the last file listed, which covers all previous files.