New Monitor or Graphics Card?

Hey everyone, so I am looking for a bit of advice. When I play games on my system, I notice that during the cut scenes and dark scenes, the screen and blacks seem fuzzy/static-like. I'm not really sure how to describe it. Also, during cut scenes, I notice a visible line refreshing up the screen which can be incredibly annoying. Does this sound like the monitor or the graphics card to you?

My Rig:
EVGA Nvidia 480 1.5GB
Asrock X79 Extreme6
2x4 GB Corsair 1600MHz Vengeance
128GB Samsung 830
500 Seagate Barracuda
Intel i7 3930k
Cooler Master GX 750W PSU

Monitor: Acer S211HLbd

I would be want to replace both at some point, but should I replace a monitor now, or just save up for a GTX 670?

I like this for a new monitor: http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Would this be the best gaming monitor sub-US$250?

Thanks for the help!