Cheapest gaming computer I could run all games on medium on.

My stock answer:
MMO's and dayZ are single threaded and cpu limited, making the G3258 a particularly good starter cpu.
A $65 G3258 with an overclock is stronger than any current cpu made for those games. That includes a overclocked $330 i7-4790K.

------------------------------ budget build ---------------------------
For a budget build, I like to recommend that one builds for future expandability.
That means paying a bit more up front for some parts that allow for an easier future upgrade.
Let me start where you might not expect:
1. Buy a good 620w psu. Such a unit will run any future graphics card.
I would normally suggest Seasonic 620w:
2. Buy a Z97 based motherboard. Z97 will allow you to install a overclockable cpu and even offer a future 14nm broadwell upgrade.
You should find one for under $100.
Here is a M-ATX : http://www.newegg.com/Product/Product.aspx?Item=N82E16813157529
3. I suggest a G3258. It is a overclockable dual core at a budget price of about $75.
Here is what it can do: http://techreport.com/review/26735/overclocking-intel-p...
In time, you can upgrade to any cpu that you want and market the G3258.
4. The intel stock cooler will do the job up to a point. But, I suggest a $30 tower type cooler like the cm hyper212 with a 120mm fan. It will cool better and be quieter under load.
5. For ram, speed is not important. Buy a 8gb kit of 2 x 4gb DDR3 1.5v ram.
If you will be using the integrated graphics, I suggest faster ram. It improves the performance. 1866 is good. You will get a WEI of 6.4.
6. Cases are a personal thing. Buy one you love. Most will do the job for <$50.
It would be hard to beat $34 delivered for this Antec GX500 :
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129191
7. The graphics card is the most important component for gaming. My usual rule of thumb is to budget 2x the cpu cost for the graphics card. I like the GTX750ti and EVGA as a brand.
Here is a superclock version:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
You could go stronger in the video card if your budget permits and your games need it.
On the other hand, you could build using the integrated graphics and see how you do.
By deferring on the graphics card, you will get a better idea of what you really need.
Integrated is fine for sims, but not fast action games.
8. Lastly, I will never build again without a SSD for the "C" drive. It makes everything you do so much quicker. 120gb will hold the OS and a handful of games. With 240gb you may never need a hard drive at all. Defer on a hard drive until your ssd approaches 90% full.

-------------good luck------------