All good advice so far. Also, a lot will depend on what kind of mileage you are able/willing to do in a day. I did the TA last year, and would always have a loose plan for the next 2-4 days in my head, and for every day, I would have 3 destinations in mind: Wimpy Day, Decent Day, and Awesome Day. Additionally, unless there was a compelling reason to stay in a certain place, I'd prefer to do a 100 mile day with a warm shower at the end rather than call it quits after 60 miles and do without. Sometimes weather, or various other factors my shorten your days, though.
All of that being said, you'd be surprised how clean you can get with just a sink or water spigot and some camp soap. I stayed remarkably fresh for nearly week in western Kansas/eastern Colorado with nothing but sink showers.