There are only two requirements for storing wheat berries:
Moisture free
Bug and rodent free
Wheat berries can be kept at room temperature in a container with a tight fitting lid.
For the best flavor and greatest nutritional benefit, use freshly-milled flour right away. You can store freshly milled flour at room temperature for no more than 3 days, in the refrigerator for up to 4-7 days or in the freezer for up to 6 months.
As long as wheat berries are unmilled and stored in a cool, dark, airtight place, they can last 30 years or longer.
The difference between hard and soft wheat berries is the protein content. Hard wheats have higher protein content and higher gluten potential than soft wheats.
If you’re making something with yeast or with a sourdough starter, you’ll want to use hard wheat varieties.