A UHD or 4k monitor needs serious graphics muscle for fast action gaming.
Not so much for slower games.
A budget of $300 for a GTX970 may well not be enough.
Regardless, you need to see what input your monitor has and match it ti the graphics card. Displayport will do the job at 60hz.
HDMI may well limit you to 30hz.
Exactly what make/model is your monitor?
I do not expect the 3xx releases to be anything special, and their price will be determined by their performance.
What is your PSU? I might think a 650w psu will be needed for a 3xx or a 290.
I think the current GTX970 cards in the $300 price range are a bit more modern and power efficient.
More like 500w needed.