When building a computer strictly for gaming some like to go with Intel for a cpu however the Intel cpu can be more expensive and so with lower budgeted builds people will go with AMD, same with the video card.
If your doing an upgrade and you want to keep the hard drive that you have then you can upgrade to this for parts.
Your choices look good, however if your going with AMD and want the top 8 core processor you should know that they make four models of that 8 core with the only difference being the stock speed. You can save $40 by going with the 8320 and you'll have the same 8mb cache and 8 cores but with a 3.5ghz stock and 4.0ghz boost. This can easily be regained by a small overclock to get to 4ghz. The extra $40 could allow for a higher model video card such as this;
This card has free shipping , a $35 rebate and free game (Metro Last Light) plus is rated one level higher then the 7850. Benchmarks have proven that an AMD CPU when paired with a Nvidia video card performs much better then when paired with an AMD card.
The CPU that you chose can be overclocked and depending on how much time you want to spend on the overclock that determines how high you can go. Some have been able to reach 5ghz but it is not easy.
AMD processors tend to run hotter then Intel processors so you do have to get a very good cooler for that processor. The one that you chose while very good will not get you very far, you might want to look at something like the Corsair H-80i or H-100i.
One 8gb stick of ram allows you to get more ram on the motherboard so if the max amount fo ram for the MB was 32gb and you only had four slots then you would want to use 8gb sticks. If your not going for the max amount of ram and the most hat you would want is 16gb the you can go with 4gb sticks. Windows will see and use the ram which ever way you go, no real performance use.
The room cooler will only make the ambient temp of the room cooler, you cannot use it to cool the CPU. It is your choice on what to do for a CPU cooler based on what kind of overclock you intend to do. The better coolers cost more.
That should work ok for you and I would put a second fan on it, the radiator can hold two one on each side. It's called push/pull with one fan blowing into the radiator and the other blowing out, it gives more cooling power. They also make the dual size radiator that can hold up to four fans.
There is a choice that some people make to give their new build that little extra boost in performance and that is to have a SSD as the OS drive and some will go with a 128gb size and others a 256gb size. If a 128gb size is chosen then they would only put the OS and the current game on it with the rest on the regular hard drive. But this is a personal choice and is not a necessary move at all.