You will be fine with the 770. You might have to bump settings down a little. Also, you can add another one for SLI and it will scream. I have 2 GTX 770 4GB Classifieds and I can hit 120fps in every game I play at full settings except I turn AA off or low.
Also, you don't have to worry about the monitor not scaling as your vid. card will scale down to 1080 if you want to. The monitor doesn't have to do it.