When reading on frame rate, i usually encounter the following suggestions:
I want to make a 2d game that runs in slow computers, and i've been surprised by how Cave Story smooth is and that it runs at 50 fps. Maybe. there is not much difference between 50 and 60, but if i dont have a reason to use 60, i'd rather set my frame rate to 50.
I'd like to know the drawbacks of this approach, specially applied to my usecase.
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).
