If humidity isn't going to be an issue, I've had success with double bagging cardboard boxes with extra large heavy duty trash bags, and taping them shut. (Using packaging tape.) It helps to mark what's inside, as you won't remember the contents a year later.

I had to contend with a leaky moldy storage shed for over a decade, and this worked to keep things dry, and keep creepy crawlies out of my stuff. I'm in California, so how well this works in other climates may vary.

The ever popular stackable plastic storage bins are also a good option.