I5s should outperform the Phenom IIs. i3 and i5 use less power and are faster at single threads than phenom. Phenoms are a match (stock speeds) or a little better (with overclocking) at multi-threaded performance than I3s but are probably lower than I5s. I5's may go past the budget.
A good start because of the price range would be the $500 system builder article from September for the Phenom II build (June 2011 was an I3. The prices may have fallen to allow a better system, but the build had sacrificed on some parts as well) . You probably want a different motherboard than the build (see next paragraph) which may add around $30. You may also need a wireless card if you don't have a compatible one already.
Get a motherboard that uses the AM3+ socket. That way, you will have the option to change to a bulldozer based processor. Currently, bull dozer doesn't appear as a good option. Perhaps with a few revisions or price drops, it could be a decent upgrade in the future.
The article's conclusion stated that the graphics card was what limited the system and better coolers (quieter) would be where to spend extra money. If you plan on going with a 64 bit OS, you may be able to use more than 4GB of ram, although it probably won't help gaming performance much. Also, a larger TB hard drive wouldn't cost much more either.
As for black friday, the hard drive comes to mind first if you're going for a large one. You may be able to find a processor depending on where you go.