Building a PC that can play games like Day Z on max setting depends on 3 main components. A CPU, GPU, and RAM Day Z is in alpha and that means its not stable, when it comes out though it will be very graphic intensive.Bohemia Interactive is making Day Z and if you haven't heard of them you might have heard about the ARMA series, 3 being the latest is very graphic intensive. I own a GTX 650 which hovers around 40 fps on medium settings. That being said that card is very cheap at about $130. I will give you a build idea below.
Motherboard this is where your components come together and make your PC, there are quality motherboards out there and many carry the for gamers title. Mainly their biggest advantage is more RAM slots and More PCI 3.0 slots for SLI or Crossfire configuration. They also allow a massive array of overclocking capabilities. The motherboard I chose is a simple and cheap motherboard made by MSI its a budget motherboard.
Intel 4th gen:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813130730
CPU not as important as GPU in a gaming build but still important which is why I personally favor the i5 over the i7 which is more expensive and doesn't provide but a small amount of more power than that of an i5.
Intel Core i5 3.2ghz
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116896
GPU probably the most important factor of a gaming build. I Chose the 760 because its a very well performer considering its small price tag. The 780 ti would be the best possible card out there but being $700+ it's not a very budget friendly. And finally the Titan which some gamers tend to claim it is the best card out there, but the 780 ti is much faster at gaming than the Titan.
ASUS GTX 760 2GB
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121775
Memory, A very important factor in games like ARMA and, hate to put this one in but minecraft, because of the large world which eats up memory faster than even next gen games like BF4. I chose G.Skill Rip jaws because for a gaming build these are outstanding. They aren't the cheapest and you could get a cheaper type of memory so look around, but get at least 8GB
8GB G.Skill gaming RAM
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231468
HDD or SSD or Both
I personally would recommend a combination of the two because you want something that opens applications fast but you also want a lot of storage for games, but since your building a budget Gaming PC stick with either the 5200RPM or the 7200RPM 1TB HDDS they are around $60 to $70 check this one out if you go for just HDD
http://www.newegg.com/Product/Product.aspx?Item=N82E16822236339
If both get a small fairly cheap 128 GB SSD for OP and a 1TB HDD for games
Look on www.newegg.com
Power supply:
You would want at least a 500w I'm sure 400w could work but it's better to have more then not enough. Look on new egg as sometimes when you buy the tower a PSU comes with some. Get either a Medium or Full tower because of the better air flow and more space. I recommend these 2 towers:
Rosewill tower with 500w
http://www.newegg.com/Product/Product.aspx?Item=N82E16811147193
Corsair tower (no PSU)
http://www.newegg.com/Product/Product.aspx?Item=N82E16811139025
This build totals at around $800 with the Rosewill Tower. This may seem a bit more than you may want to pay but if you get cheaper RAM and maybe downgrade on the size of the HDD and even find a cheaper Tower you could be looking at a Price around $600 or $650, but try not to downgrade to the i3 or a GTX 600 series graphics card as those would not provide you the FPS you are looking for.
Last but not least another option would be to go with AMD, I am not an Intel/Nvidia only Fan, but i do believe Intel and Nvidia are for right now the better choice. You may actually want to wait for AMD's Mantle as it may end up being the winner for graphics, be aware that mantle isn't out and is only supported on the R9 series Radeon cards.
Hope this helps and good luck on your build.