Glad to have helped!
Note that this monitor doesn’t have a VESA mount, if that’s a factor. You can work around it, but it’s more expensive in total than buying a VESA monitor.
https://smile.amazon.com/ASUS-VX248H-1920x1080-Gaming-Monitor/dp/B00GMGHCVG/ref=sr_1_1?s=electronics&ie=UTF8&qid=1533043019&sr=1-1&keywords=asus+vx248h
Refresh rate is the number of times per second that the screen is repainted. Think about flip books, if the pages flip by fast enough, the images look continuous. If this rate is fast enough, we (humans) aren’t aware of the flicker. This can vary from person to person. Some people are bothered by 30Hz, or even the flicker of fluorescent lights. I prefer 60Hz.
As far as I know, HDMI only supports 30Hz, so I opt to use the DisplayPort and a usb-c to displayport adapter, as outlined in the post I linked above.
With a max budget of $500, I would go for a 4K display. I find the higher number of dots to be less fatiguing for my eyes, displaying smoother text and images. It also gives you flexibility in changing the scaling, so you can opt for more space or a larger text.
This thread and others here on the forum may be helpful.