respond time always not actually the monitors has...

every monitor got its input lag+respond time, dont fall into marketing trick @@
Survey more about review an monitor which more details

Refresh rate and g-sync/freesync is another story and depends on your gpu performance.

Input lag and respond time is totally different things....
Input lag is command from ur source output to ur display, respond time is how long your display process to visual.

Commonly, a tn panel respond time will be 1ms-5ms, ips panel 5-8ms, va panel about 10-15.
Input lag is vary coz every display has different timing, Usually, a tv's input lag more than a monitor does, and higher resolution the input lag commonly will more.

one ips monitor may have similar input lag with one tn display, even a tn panel of 1 ms may higher input lag.

example,

Samsung u28d590d 28 inch 4k tn monitor stated as 1ms monitor, actually its respond time g2g can reach highest as 19ms, lowest 1ms, average is 7ms. Its input lag can reach as high as 39ms.

Acer xb271hk 27 inch 4k ips monitor stated as 4ms monitor , it got respond time lowesr 4.5ms highest 11ms,average is 7.6ms. But its input lag just only 4ms.

Don't be fooled by marketing 1ms 6ms 8ms, its actually a bullshit. Just survey hows your current display performance under review, if willing to change a display, pls surevery as more as possible to get a best value for fit ur budget.