Could a basement make animals sick?

I want to move into my basement but my mom is saying that the moisture can make my animals sick? I have two chinchillas and two dwarf hamsters that will be in the basement i am keeping my guinea pigs outside. If chinchillas get wet they can grow mold on their fur. I do have a heater and there is a fireplace down there so it wouldnt get to cold for my hamsters. Also would my clothes smell? And if they would what could i do to prevent that? Thanks!!!!