I used this case for my buildout. It's small, but supports full-size graphics cards and multiple internal hard drive bays. It's more or-less invisible on my bookshelf next to other components. It also doesn't have any drive bays, which looks very sleek and I just download everything from Steam (or similar) these days anyway.
Yes, that's exactly what I already had in mind. To be honest until yesterday I didn't even realize that Mini-ITX could handle the newer sockels and a decent PCIe graphic card. But with knowing that, this is a very good alternative to a console.
http://www.newegg.com/Product/Product.aspx?Item=N82E16811112...