I really don’t think the moisture would be a big issue. I do suggest installing a quality fan. I’ve installed several fans in my time. I recently installed a “Hunter” fan in my bedroom.

This fan far surpasses all others I have installed. From the installation manual to the noiseless operation, it is flawless. It doesn’t wobble a bit and won’t break the bank. About $70.

There is a great warranty associated with it too, though I can’t remember the terms of the top of my head. Good luck.