The typical issue with basements is moisture, especially in the summer/humid months. That moisture can lead to a 'musty' smell. If you use a dehumidifer and keep stuff off the floor, you should be OK.
Here are the specs of the room I use for storage:
Basement room with no direct heat. (Forced air heating is only upstairs in my house)
100% light free (window covered with room-darkening blinds and door shut), except when I am in it
Dehumidifier running non-stop in the summer to remove as much moisture as possible
Carpeted (This helps keep the moisture away from the Lego I store on shelves. I do not place anything on the carpet itself except for storage totes that are used to store Ziploc-sealed lots of polybags.
I do also keep a couple DampRid-style jugs around the room. I use these personally to non-scientifically judge the moisture level in the air. They essentially grab moisture from the air and pull it into a container. If they are collecting a lot of moisture, I adjust the settings on my dehumidifier.