The $600 build in that article is very similar to what I put into my machine. It has the exact same processor and the GPU is an AMD that is pretty similar to mine but a newer model. There are a few differences like my 8GB of ram vs their 4GB and I have a beefier power supply and SSD but overall it's pretty comparable. It's slightly higher than the $300-$500 range you mentioned but it has a much better graphics power than the AMD APU in their $300 build.
The $300 build would work great for games you have mentioned like Minecraft and Don't Starve. It would play more complicated games like DayZ if you turned the settings down. If you can swing it you will be much happier with the $600 build. That is on the level of the new consoles or slightly higher. We are talking 1080p with high settings for pretty much everything.
One thing to keep in mind... Sites like Toms Hardware frequently use the PC Part Picker tool too. For some reason they never include the cost of Windows though. You could instal SteamOS instead of paying for Windows but I don't recommend it. If you do that you will only be able to play games that have Linux compatibility. That is just a small portion of the games in the Steam store and most of them are indie titles.
When you are looking at these prices keep in mind that you will probably need to add in $96 for a copy of Windows 8.1 so that $600 build is really closer to $700.
http://www.amazon.com/dp/B00F3ZN2W0/?tag=satell01-20