Refresh rate matters, but it is only one part of a good display. Resolution, panel response, contrast, variable refresh support and the performance of your PC or console all affect what you actually see.
For most players, a dependable 120–165Hz screen is the useful middle ground. Competitive players may benefit from more, while slower single-player games often gain more from image quality and strong contrast.
Match the monitor to the games and hardware you already own. Paying for a headline number that your system cannot sustain rarely makes a sensible upgrade.