Unfortunately, that SFF PC only has a 240W PSU with a +12V rail rated for 17A. Pretty weak to try adding a discrete card. But the HD 6450 is only a 31W card. That should only present a 2.6A load to the PSU, and should be fine.
But to get the best gaming performance w/o overtaxing that little PSU, I'd suggest the 25W GT 730 low profile card. But be sure to get the 64 bit, DDR5 version. And be sure to check that the single slot card doesn't extend its width too far to squeeze in the confined space you have available. Some cards' cooling shroud bulge out quite a bit and make the card a bit wide.
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&IsNodeId=1&N=100007709%204814%20600038363%20600038364%20600007799%20600519936%20600007797
Here's a comparison of the performance of the HD-6450 vs GT 730: http://gpu.userbenchmark.com/Compare/AMD-Radeon-HD-6450-vs-Nvidia-GeForce-GT-730/m7821vsm12582