You absolutely must install a vent fan to take moist air out of the basement all the time. I've been to a home that had three big aquariums in the basement, and the entire foundation of the house was at risk. The finished basement was soaking wet and the floors were buckling due to all that moisture. The owner was planning to add an air conditioner, but I strongly urged him to add several vent fans immediately to alleviate the problem.
With ventilation, you shouldn't have mold issues. You may find that that occasionally you can switch them off, but I would expect them to be running around the clock for most of the year.