So with Fallout 4 coming out soon, I've been thinking it might be time to upgrade my PC. Right now, I have an i5 3570k CPU and a GTX 570 graphics card. I think the CPU is okay, but the graphics card probably isn't. I'm looking to be able to play current games at 1920x1080 and stay at or near 60 FPS on medium-to-high settings (for reference, I think vanilla Skyrim looks good enough even without Bethesda's high-res DLC, so I don't need top-notch graphics). I'd prefer not to go too far over $300 for the upgrade, if possible.
So I'd appreciate some information of whether or not this is possible, and hopefully some recommendations on what graphics card to get.