Air flow is the best way to minimize musty smell. Use wire shelving, and don't stack things - in other words, have enough shelves that things are stored only one item deep.

Closing stuff in bins tends to result in the stored items smelling like plastic.

I store some things in weatherproof crates (which also helps to keep bugs and rodents out) with large dessicant packs inside. I make sure to open the crates and check things out at least twice per year and replace the desiccant packs at those times. I think you would have to experiment a bit to see what works best in your area.

I don't remember what brand of desiccant packs I've bought. I get them from Amazon. The crates are from Container Store found HERE.

Before you store, make sure it's really dry.