not too much to add to what everybody else is saying, other than three things...
polyester dress shirts - no matter how awesome it looks, polyester that is repeatedly perspired in will eventually (and permanently) acquire a stink that cannot be hidden, removed, or in my opinion, tolerated (somehow worse than standard BO). Wool doesn't have that problem. (or if you must go with synthetics - trash them based on smell, something I do not advocate, or only wear them for smelly endeavors)
On washing up: I pack an extra hanky or washcloth with me. If you have no access to fresh water, I suppose one could moisten at home and take in a plastic bag (one could even pre-soap one) but I usually don't. Like a wet wipe, but produces less trash, comes in any color imaginable, is far less expensive in the long run, is totally customizeable, and can double as a snot rag (wipe self THEN blow, wrong order is icky).
On days like we've been having, sweat seems inevitable unless you're driving an airconditioned car from one airconditioned, attached garage to another. It's all about the smell, which is easier to avoid than you'd think. Never under estimate the power of baking soda on a powder puff. My husband (proud of his sensitive sense of smell) is a total convert and holds it in higher regard than regular deoderant (and one can apply it to the inside of stinky clothes with less visual detection). I love it too, but I'm a cheap hippy.
Hope you figure it out and find pleasure in it, it sounds like a very pleasant commute!