I have a ACER AX1700-U3700A with the slim micro-ATX case and I searched for a while for a video card upgrade.
The best bang for the buck was a $69 Saphire HD 5500 video card that has a silent fan, low power consumption (no external power connector), PCI-express 16x 2.0, 1 GB of DDR3 RAM and is built in an ultra-low profile config. It comes with the full Profile bracket and the Low Profile bracket so you can just unscrew one and attach the other.
I had the a 512mb nVidia card that came with the computer, but it was stressed out by newer games. For example new Starcraft II would play okay with all settings on minimum. With the new card the same game would play with settings on high very fluid.
Assassins Creed would play with lower settings but slow down and drop frames, and with the Saphire card it plays fast with everything on maximum.
I just got Civilizations 5 and I can play it with direct X 11 and all settings on high.