I just built a tiny (I can fit it in my backback no problem) gaming rig that is registering 7.6-7.9 in all Window's performance categories (not sure how great that is). Almost all are 7.9 except the CPU, which is at stock speeds right now due to cooler issues. My computer flies, I'm absolutely thrilled with the performance (sans 1 vid card issue I'm having at the moment).
the mobo I used (works very well):
The case I used:
Cooler Master Elite 120 Advanced
This case just blows me away. With my enormous video card (HD 7950 Sapphire), two HD's, full size ATX power supply, it's pretty much filled up to the max. They really managed to make a tiny case that literally fits everything you need with no room to spare. High quality, looks nice. I'm going to slightly modify it (cut the bottom of the HD cage to fit a liquid cooler radiator underneath it), but other than that, it's absolutely perfect. And only $40-50, such a steal.
screen size is not important , only the resolution .
A 560 ti will play games well at 1080p resolution so it is going to work .
It should easily fir that case , and so will a standard ATX power supply . See the article I linked to about how long the psu can be .