I'm a big fan of a backpack stuck in a milkcrate on a rear rack as far as transporting stuff to work. I like the idea of panniers, but I've never been motivated enough to spend the cash.
Re: your specific question on transporting clothes, though, I'm afraid I can't help much. I leave my work clothes at work and change in my office. Like other folks have said, I don't find showering necessary (I live in Florida) because my commute is relatively short (5 miles), flat, and I'm used to it. I also don't go so fast.