Just for personal preference and the fact that a 24" monitor should be a better native fit for movies I would go for that. There is a little more to it such as I would expect the 24" model to have smaller actual pixels which means you can get closer to it without being able to notice the pixels themselves.
Sitting to close to a large screen monitor is a mistake a lot of people make, you can end up loosing a lot of perceived picture quality by doing so. There are recommended viewing distances on line.
As I said most people sit too close and that would be for a smaller screen.
The fact that people are to close is usually a space issue and with a PC its not really practical to sit much more than about 3ft away. If you check the viewing distance on line you will find a 27" screen ideally wants you a bit further away than that as does a 24" screen.
Also as far as the build goes i would say you want to ditch the case and get a decent gaming case. I have a Cooler Master Elite 430 Case upstairs and I would call it a midrange case at best. I'm not even sure a 6970 will fit in it. I do know the cooling wont be up to the job though.