What about a 4-gig 770 or 760?
The ram on a card is usually for High Definition textures 1080p and 4k. It really depends on the processing power of the GPU to render certain things in real time such as shadows. 4GB is recommended for most "Next Gen" games. The 700 series are Kepler GPU's, the current generation of graphics cards. Nvidia has different generations of graphics cards they name off of famous and innovative inventors. Such as Tesla, Fermi, Kepler, Maxwell, etc.
A GTX 770 4gb is a perfect choice for performance and price. I would get a 770 with dual fans. The stock card heats up to 70 degrees Celsius, or 158 degrees Fahrenheit.
I am using 2gb, and runs most things fine, just some issues with games at higher texture resolutions.
