The AM3 socket was not current for long.
The best chip made for that socket was the Phenom II x6 1100T. New, you could find them for $200; but they're only available on E-bay now... for $170-$200 used. The 1100T could be overclocked quite well, so with a good CPU cooler, and a solid motherboard you could get pretty good performance out of it.
However, for the price of that chip, $200 or so, you could get a FX6300 AND a new good motherboard to run it on, or spend a bit more and get a Haswell i5 and motherboard,
What you have is a decent chip. There is no 'super' upgrade available.