You leave too much information out. Your CPU? Your power supply? New cards or used?
In general, around $100 is the starting point for new gaming cards. For example, the RX 460/560 and GTX 1050. These cards can run all modern games at some combination of settings/resolution and get you 40fps or more.
At the $60, realistically in new cards you're looking at 30fps low settings 720p, IF you're lucky. Some modern games won't even run that well, with lots of stuttering and framedrops.
At $60, in used cards you could get something similar to what $100 gets you new. Something like an HD 7850.
This only works IF you have the CPU to play modern games AND you have the power supply.