For the cheap dual core route I'd get a X2 4000+ 1MB cache if they're still available out there! Most of the X2's only have 512k cache but there used to be versions of the +4000 out there that had 1MB cache and the more cache is always better in the long run. If you can't find those anymore (I havent looked at the AMD CPU market in awhile as an Intel Core duo is my next upgrade) and you going for a cheap 939 CPU thats dual core to boot i'd go for at least the X2 3800+ as they were very cheap after the price cuts a few months ago and I only imagine theyre cheaper now with the Intel Core 2 duos out there. Plus they overclock fairly well. A cheap, great overclocking chip I can vouch for are the Opteron 144's (single core) as I got one back when they were THE chip and its been OC'ed to 2.9ghz on water since. With the prices of dual core AMDs these days and more and more programs/games being optimized for them I think any CPU upgrade should be at least dual core at this point if you plan on getting the most mileage possible!
Unforunately i'm out of a video card right now (power surge killed it!) so i'm missing out on my gaming but if you plan to overclock and you're a gamer i'd go for what I mentioned earlier. If your NOT going to OC and cash isn't an issue i'd go for a higher clocked dual core X2 or Opteron at this point if your limited to a 939 mobo.
Edited for spelling/clarification.