Good gaming pc 500-600 dollars?

Well, you won't be running DayZ smoothly enough with a $500 rig before you stress out. You could probably run it with a $600 but that's it.
And no, you won't find any pre-built PCs in the internet that costs $500 that can run DayZ, you'll have to build it yourself, it's quite easy, it's cheaper, you can add whatever you want and can be more powerful.
If you seriously don't want to spend $600 and you also don't want to build it, then I'm going to link some PC that costs $500, keep in mind that most of these won't run DayZ smoothly:
http://www.newegg.com/...6883227510
http://www.newegg.com/...6883229362
Buy this and you'll get BF4 for free!: http://www.newegg.com/...6883220562
http://www.amazon.com/...00I48Q9LO/

I could mention more but they were more expensive.

Anyways, these were the cheaper "gaming" PCs that I could find, all of them will run Minecraft, but you won't be running DayZ without constant FPS drops. And I wouldn't wait until DayZ comes out of Alpha since Bohemia Games are the worst optimized games, so don't expect DayZ to run smoother by then

If you want to build it, I used this website: http://pcpartpicker.com/parts/partlist/ to select my components. You can chose anything you want and then you can go and buy them from the best online store there's.
If you don't know what to chose, I made one already that costs around your budget: http://pcpartpicker.com/p/3E6gF

Again, keep in mind that it won't run DayZ so smoothly in any settings since it's really bad optimized.
Hope you get what you're looking for, update your answer if you have any more questions