My commute is about the same distance as yours. I can dress fairly casually at work so I just ride in what I'll wear at work. I find I don't get sweaty if I go at a moderate pace (zooming just gets to more red lights faster) and its not the middle of a heat wave in summer. (when I usually bring a change of clothes)

For this wet and mucky weather I wear a waterproof k-way jacket, and some rain pants that I pull over my other pants. If its raining lightly my helmet keeps my head dry enough, if its heavy I'll put a rain hat over the helmet. I usually bike in old running shoes, and keep some decent shoes in my desk drawer at work.

The fenders (full ones with mud flaps) help but I still like the overpants if there is any muck on the roads because even if you don't spray it at yourself a passing truck may end up splashing you.