For me, must haves are:
Eye drops to wash out my eyes. Even with sunglasses on, once in a while I get grit or, worse, a bug in my eye. Being able to wash it out is imperative for the rest of the commute.
Hankie: In the summer, to wipe off my face when I arrive at my destination, in the winter to blow my nose when I come to a stand still. (What makes that always happen?)
Lip balm: self explanatory, I think you said 36 miles round trip, right?
Happy and safe commuting to you.