GTX 670 which I had is almost the same card and it does well @ 1080p with high settings excluding the most grueling games so a lower resolution will be ~ 35% higher fps/1080p.
Only reason I brought up 770 is because they are going to drop in price soon with the 960 launch and there will be some killer deals for more horsepower, I always assume performance and value are the two most important things.
Also: Keeping that monitor is fine because with an NVidia GPU you can render games at higher resolutions for higher image quality, I enjoy playing games on my 1080p screen @ 2k-4k depending on performance.