A great way to shave money off of a minimalist system is to skip buying a GPU and using the one present on modern processors, as well as installing Linux instead of buying a Windows license.  The problem with doing so is that playing demanding games is going to be beyond your computers ability, at least without turning off most of the features that make the game look good.  To help you figure out what your machine would be capable of is this article from Phoronix.  Their tests show that Windows 10 currently has a very large performance lead compared to the same hardware running on Ubuntu as the Windows OpenGL driver is superior to the open-source Linux driver.  This may change sooner rather than later but you should be aware that for now you will not get the most out of your Skylakes GPU on Linux at this time.

"As it's been a while since my last Windows vs. Linux graphics comparison and haven't yet done such a comparison for Intel's latest-generation Skylake HD Graphics, the past few days I was running Windows 10 Pro x64 versus Ubuntu 15.10 graphics benchmarks with a Core i5 6600K sporting HD Graphics 530."

Here are some more Processor articles from around the web:

Processors