Whole grains have a higher gelatinization temperature than starch as a whole. Whole wheat gelatinizes at temperatures closer to a boil while wheat starch easily gelatinizes around mash temperatures. This is why wheat is known for giving terrible efficiency. Adding to the problem the problem is that wheat is smaller and harder than malted barley so our mills are not normally set to effectively crush it so you get poor surface area from milling the wheat.
A fine crush will take care of the issues mentioned above, because the wheat starches themselves do gelatinize at mash temps. Also, soft white wheat has fewer proteins and more carbohydrates, so I'd suggest this variety unless you want to do a protein rest.
I had an old corona mill, which is actually designed to be a flour mill, and I could crush wheat berries to almost a flour with minimal effort. And by minimal, I mean "I'm sweating my ass off and feel like I'm going to have a heart attack" after 4 pounds. Now I have the kitchenaid flour mill attachment, and can do about 4 pounds in 10 minutes.