I am looking to build a mid grade gaming pc for myself. I want it the sise of a xbox one or ps4 so that I can put it in my backpack and take it to friends' houses for lanparties and hang outs. This is what I came up with and suggestions. I have a buget of $750. I know that I can get a better bag for my buck because of the up coming holiday season.
You would probably be better off making your own custom case, there really aren't many options using an itx case(with the exception of the Prodigy, but it's pretty much as big as an mATX case)
Not as small as the new consoles, but it should fit in your back pack and keep your components from overheating.
I chose the Athlon because the FX-series really isn't viable in an mATX/ITX motherboard because the VRMs are usually sh*t. The Athlon paired with that motherboard and cooler will be amazing at overclocking(might even beat the 8320 if you hit ~4.2GHz).
The R9-280X will perform much better than the GTX 760, allowing you to max out any game at 1080p.
My own gaming rig is stuffed in a Factal Design Node 304 m-ITX case. Quite a bit smaller than the Prodigy and a better interior layout IMO. The Node even allows for tower CPU coolers like the Hyper 212 and some all-in-one liquid coolers. It also has plenty of options for storage placement and it will take any full sized GPU, no problem.
If you go with an m-ITX form factor, you won't be able to run an FX CPU because there are no AM3+ m-ITX motherboards. Nobody makes them.
If you want to stick with a more xbox-like shaped tall and narrow enclosure, you'll have to find another case that works or build your own case and use a PCIe riser for the GPU like jammy suggested.