Specifically for display refresh rate, it's not really much of a choice, it's more of a mandate, and there's no reason not to go for this. The reason is that
a lot of underlying technologies / rendering engines opt for syncing with the hardware (vsync) which typically updates at about 60Hz (this figure primarily for historical reasons - it was closely associated with the frequency of AC current in the days of analog television - see PAL / NTSC).
Understand the reason behind vsync: Without it, you may get partway through painting a frame before a hardware update triggers, leading to tearing that you may have seen in windowed games. At best, you'll get frames that don't tear, but also don't sync nicely to your monitor's rate, resulting in a less-than-ideal feel.
Also remember that your logic update rate is not mandated by your visual update rate; but if your main loop is driven by the display refresh rate, as in e.g. Android, then best make your logic update evenly divisible into display rate, e.g. for 60Hz display refresh, it's easy enough to do logic 1 in 2 frames (30Hz), or even 1 in 3 frames (20Hz).