You can get a dual core for $300 (X2 3800), but you need to understand something before you buy dual core.
For most games right now, dual core is useless. The dual core you select will perform as well as whatever the single core equivalent is for one of the cores on the dual core. This is because games by enlarge are not optimized for dual core.
Case in point, the X2 3800 is 2x 1.8GHz cores with 512K L2 cache each. That means for most games, the dual core will perform as well as an Athlon 64 3000 (1.8GHz with 512K cache).
The reason I recommend an Opteron 165 is it is only $30 more than the X2 3800, has 1M cache per core (puts it closer to the Athlon 3700 in performance for things that are not optimized for dual core), and it overclocks very well. Most can overclock it to 2x 2.5GHz cores, which couple with the cache would allow this CPU to outperform the Athlon 64 3700 unless you overclock the 3700.
Once games are effectively optimized for dual core, the Opteron 165 will destroy the Athlon 64 3700 in performance. However, you must realize for now it is $100 more and will not give you much performance advantage over the 3700 in games.
For your PSU, make sure it has the right connector for the motherboard (20 vs 24 pin). You can always get an adapter. 500W is ample for the system it sounds like you are gonna build.
One last point that should be said - your video card will make more of a difference than which CPU you decide to use for gaming performance.
If you have an Sempron in socket 754, to be honest, I would consider waiting. Sure it is not the best CPU, but I suspect you will find the upgrade a bit disappointing performance wise.
I did check CPU prices for socket 754 for a good upgrade to something with 1M cache, and you definitely shouldn't go that route. $330 was the price for the S754 3700, which makes that CPU a silly upgrade for the money. (S939 mobo is $100, and the 3700 S939 is $230, duuuuuuuuh!)
"Milk was a bad choice!"