+1 for Intel HD 4000
I have recently built a small system for the kids to install Ubuntu on. It is based on an Intel Core i3-3225 CPU with built in HD4000 graphics. Built it, turned on & installed OS. No proprietary drivers. No added PCI-E card. 20 to 30 Watt power usage and it all fits inside a Antec ISK110 case. 3D games like Puzzle Moppet as well as Google Earth works better than on the previous Nvidia Ion2 system I used for the kids.
I initially bought into the AMD/ATI opensource drivers hype which did not work out as planned - for me anyway. Let's just say I am unlikely to ever buy an ATI card again. I then went back to Nvidia but although the drivers worked well on my main debian systems as well as ubuntu there were always additional tweaks and issues with adding the proprietary binaries. This however, was the most pain free custom PC build I have ever done as far as installing Linux is concerned. The only reason I can see currently to use an added ATI or Nvidia video card is for a high end Windows gaming PC.
PS the mini ITX motherboard was an AS Rock H77M-ITX. Everything was detected and worked out of the box.