Ok, not many people have brought up everything as far as the main components in a gaming computer go.

First off, graphics cards. That is something you CANT go cheap on for gaming. Most games do perfectly fine with a 1gb graphics card which is almost standard now, but it is still something to look into.

Next would be the processor. Anywhere from an i5 to an i7 26-3300 should be fine. Once again, i5's are pretty common now. (At least i think they are) So you should be fine there. I dont know much about AMD processors and so on so i cant help much outside of intel.

The last thing that keeps games running strong is the Ram, or memory. (Not storage) Once again, most games run pretty well off of 2 gb of ram. Just another thing to check.

With the bare minimum of what i have listed above, the games you listed will me more than fine. I am on a laptop with an i3 processor and 512mb graphics card. I run minecraft with 30-60 fps thanks to optifine. I hope i helped!

~Hydro