Consider burying a galvanized garbage can in the ground to create your own "root cellar." The root cellar keeps potatoes, carrots, beets, turnips, and apples through the winter. Bury the can upright with 4 in. or so of the top protruding above ground level.
Place the garbage can on a well-drained site, and make a ditch so surface water will be diverted and not run into the container. Make sure the can has a good lid, and cover the lid with straw. Over the straw put a waterproof cover of canvas or plastic.
Put veggies and fruits in perforated polyethylene bags. Root crops like beets, carrots, and turnips should not be put into storage until late fall. Don't store carrots near apples because the apples give off gases that make the carrots bitter. Avoid bruising veggies to prevent rot. Also, I don't recommend sweet potatoes for the "root cellar" because the dampness causes them to decay.