I really don't think any GPU with over 512mb memory is going to run into any bottlenecks on the desktop, even watching a video. You are going to want the cheapest card with the outputs you need (sorry don't know exactly which card that is )
I normally don't recommend one GPU manufacturer over the other, but my old ATi (AMD) setup had a similar problem to what you described. It turned out the cards were downclocking way too low in 2d mode to save power, and couldn't drive the multiple high-res displays properly. For this reason, I would recommend getting an Nvidia card instead.