Hz, short for Hertz, is, in this case, referring to how many times per second the screen is redrawn. 60Hz is standard for LCDs. Back in the late CRT days, 60Hz was considered an affront to the eyes and we tried to pick resolutions our monitors could run at 85Hz, or 70 Hz in a pinch.
LCD displays have different characteristics than CRTs. The pixel light persists a bit when refreshing, so 60Hz is acceptable for general use. Gamer targeted monitors can run at 100Hz on up to 240Hz, with diminishing returns as you move up the scale.
Faster refresh makes motion on the display appear smoother to your eyes. Most people can tell the difference between 30 and 60Hz, quite a few can tell from 60 to 85, it diminishes rapidly past that.
The GT 1030 will probably work. Since you don't game an entry level used Quadro 4GB card is an option too.
The other problem with upgrading your GPU is that the cards you're looking at are likely to be totally unnecessary in your next PC, so you'd be better off putting the money into the next PC instead. With the market you're shopping in, the price/performance curve is unlikely to shift significantly during the course of the year.
Was searching for 4GB 1030s (which don't seem to exist) and saw this. Look for a GDDR5 card if you end up picking up a 1030.
https://www.forbes.com/sites/jasonev.../#21b49f7793d9