Favorite grain storing container for my kitchen: The Mason Jar. I love the half gallon version. They line up on the pantry shelf perfectly.
It’s more than important to store grains well. Whole grains need to be stored more carefully than flours and cracked grains. The bran and the germ of whole grain contain the wonderful nutty oils that spoil and go rancid. Heat, light and moisture will all start the breakdown process, so keeping grains tightly closed in jars in a cool, dry pantry away from direct sunlight is the best care you can give.
You will often hear that milling makes grain more shelf stable because separating away the bran and germ reduces the rancidity potential. What that means is not that you can store flour for longer than you can whole grain — because you can’t . The noodles and breads and pastries that are made from milled flours get the benefit of all that shelf stability. Milling and grinding strip away many of the rich and vital nutrients that make whole grain SO whole. And, grains lose their nutty flavors when cracked and ground. Processed foods and baked goods no matter how whole grain they say they are will just never quite have it all.
There is more to be said and done on the topic of storing grains. I’m not a fan of refrigeration and definitely not of freezing (because I am not a fan period of freezing food) for normal grain storage. Refrigerating will increase the time and freezing may double it. But whole grains are a lot more shelf stable that we generally give them credit for and really can be kept when stored well for years.
The rule of thumb is this: Store whole grains for 4–6 months in your pantry. Store flours for up to 3. I've personally stored whole grain longer than a few months so I do know they last perfectly well for even a year. Close your jars tightly though! Bugs love grain and flours. If not sealed up, those little critters will find their way to your food first.