Wheat is one of the recommended grains for longer-term storage. It has a shelf-life of 30+ years. And like the Word of Wisdom states, grains are "the staff of life."
There are several different kinds of wheat:
Spring or winter -- which just refers to the season in which is was harvested.
Hard or soft -- hard wheat mills more consistently and has more protein (gluten).
Red or white -- which comes down to taste & texture preference.
You really have to figure this one out for yourself. My personal preference is hard white wheat. You may not know what to do with wheat, but don't let that stop you from storing it. My recommendation is that you acquire your wheat and then figure out how to use it.
In order to take advantage of that 30+ years of shelf life, though, you have to store your wheat correctly. Choose storage methods that help you avoid moisture, light, heat, and bugs. I personally use food storage buckets. I buy my wheat from Lehi Roller Mills. The wheat is clean, prepackaged and stored in a bucket with a gasket. Wheat prices are super high right now. I noticed that Costco is selling a 45 lb bucket of wheat for about $28. Last year, I bought the same bucket for about $17. I've heard that prices should fall once additional crops are harvested. The church cannery sells wheat in bulk and in #10 cans. Their prices are typically competitive. Some wheat comes in sturdy bags that are meant for storage (they are typically labeled "for storage" if this is the case). You can also seal your wheat into mylar bags within plastics buckets (ideal, in my opinion). If you buy your wheat in bags, you'll need to transfer and clean your wheat using a dry ice treatment. Instructions on how do this can be found here.