Monitor options for more than just gaming (with a less than beefy GPU)

I currently have a triple monitor setup with a 21" 1080p IPS Acer monitor and two 20" 900p TN Hannspree monitors, and I have the opportunity to spend up to $500 or so on a nice new monitor. I don't game a ton, so the new monitor will mostly be used for TV/movies and programming. I'd obviously like to game on it, but I only have a 2GB GTX 760, which barely gets 1080p60 in newer games.

So does anyone have experience with a monitor that their PC can't exactly handle in games? If I go for 1440p, would I be ok rendering in 1080p and displaying in 1440p, or will I be stuck with my 21" Acer for games? Is 1440p any good for movies when most are only available in 2k? Is there any point in going for 120Hz if movies are captured at 30fps and I can't get those extra frames from games? Would I be better off sacrificing vertical resolution for 21:9?

So what are my options, tek syndicate community? I'd love to hear what solutions you guys have come up with for displays where gaming is not the top priority.