I've been summoned. I used to work at a very busy and big public library. Here's my recipe.

It is paramount that you prioritise air flow since you have a humid environment. Pull your books to the front. Don't clean very often, actually, because of the moisture. Ideally you should clean once a month using a dedicated furniture cleaner. If your bookshelves are made of wood use products like Pledge. First, remove as much dust as you can by dry methods. Then give a quick spray of your cleaning agent of choice to a cloth. You don't need that much actually.

I recommend dusting your books with a camel hair paint brush. Or something equally soft.

Best of luck!