Glass jars, see above. Almost everybody buys things that occasionally are in glass jars and they are perfect for recycling for storage! Just wash them make sure they're dry and fill with all kinds of things like beans, pasta, Etc. For some foods you can use O2 absorbers.
Baskets, they're great, whether wicker, plastic, wire, or metal, all can be used to store lots of things-
Vacuum sealed bag. I have one of these machines and they work great! While I primarily use these for the freezer I do occasionally use them for dry goods like nuts. They're a little bit of an investment initially but I noticed that they have completely eliminated any freezer burn on meats and things. I have frozen some for up to a year with no damage.
Plastic Ziploc bags. These come in handy if you have things that you want to store in a more flat way, like bags of chop nuts that you want to freeze. Put them in a ziploc bag, get out as much air as you can, roll them up, label and put in your freezer. Ditto to lay on the shelfs.