You can have a good or an entry level, if you like, gaming rig just with the APU (720p gaming) or include the Radeon 6670 for dual graphics or Hybrid Crossfire for a bit fancier gaming experience. You can cut some of the costs if you have an old case lying around, but don’t use a cheap-ass power supply, unless you want to destroy all those parts or your house. (also add the cheapest no-name no-brand optical drive, forgot to include that in the image above add 10-15€)
I know the prices are in Euros but you can search your local market for the same parts and compare the prices in your country's currency. DO NOT JUST CONVERT THESE PRICES TO ANY OTHER CURRENCY, because hardware may be cheaper where you live.
This system can be overclocked for some extra performance if needed, but you may need to buy better cooling for the CPU. You can also get the AMD A10-5800K for a bit extra $$ and add a larger drive ( >500GB). This system has room for future improvements, for example you may one day have an extra $200 lying around. You can sell that 6670 on ebay or something and grab a better graphics card that can handle bigger resolutions and higher graphics quality settings. Or add a super fast SSD or two on RAID-0! Gaming-wise, the CPU won't make any difference it's the graphics card that will do. The A8 APU has an embedded GPU side-by-side with the CPU, (all-in-one chip) that's not powerful enough for high resolutions and high quality settings, but coupled with a dedicated card it will deliver the performance needed for any games.
I've setup a couple of these for some friends and got positive feedback. Beside games, this system can be used for every day stuff like internet surfing, document editing, music, 1080p movies, etc. Don't expect to do 3D graphics or movie editing. Not that it can't, but it will be a slow process.