I have the GTX 660, I guess the 770 is the newer or better version of mine. From what I have experienced Nvidia make a fine graphics card and I have seen good reviews of the 770 online so I would get it if I were you.
I'm sure it will be. My 660 runs games on ultra high graphics no problem. You should make sure you have a good power supply, motherboard and plenty of RAM for optimal gaming.
It would be better to buy the 970 instead if you want a video card that is cheap. It will be great for 1080p and also 1440p if you wanted to upgrade to a 1440p monitor in the future.
Edit: Unless you rather junk out $650 you could get the 980 Ti. It is 4k ready and as powerful as the Titan X which is a $1,000 video card.