I just store mine on a shelf in my climate controlled basement. It ranges from 25% to 70% humidity throughout the year. I've never had any problems. I've bought dies with rust that needed to be cleaned up, but I've never had any rust problems come up. When the humidity starts to creep up over 70% I use a dehumidifier.
Any oil should work for rust preventive. The heavier the better for staying put.
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