Do NOT buy a pre-built computer from Cyberpower. here is what you should look at. its on the low end of your budget, and will run EVERY game you want to play without any issues...even the most demanding current AAA titles. I based this build off of the things you've mentioned in this thread...so it's a proper foundation for a enthusiast level PC.
Look here:
http://pcpartpicker.com/p/hdV3Bm
it's an overclockable CPU that will allow you to dabble in overclocking when you are ready. The motherboard is z87 instead of the newer z97. Other than a few extra connectivity options, there is absolutely no difference in performance. It saves you some coin, and you only lose out on external sata and things that will likely be useless to you.
I used the parametric filter to select a few options for you, it means these are auto-selected based on parameters and real-time market pricing. those items might change from day to day. but as it stands, it has selected some terrific RAM, and a great GPU also.
I have included an AIO water cooler in this rig just for giggles. if you decide you want to overclock it, this is a decent way to ensure a better experience. It's by no means as good as proper watercooling, but its better than pretty much any air cooler. you can use the stock air cooler that is included with the CPU if you'd like.
I left the rest up to you. Everyone has their own preferences in mouse, display, keyboard, speakers, OS, etc. do with those as you please.