+1 on fenders, they go a long way toward keeping you and your bike cleaner. In Tucson I wouldn't invest in anything more than a cheap rain jacket. I commute in Portland, and seldom wear rain gear. Maybe 10% of the time in winter at most. Even then it's only a jacket. Most of the time a water resistant windbreaker is sufficient. Also a helmet cover is good, but you can use a shower cap. Neoprene socks work well if it's cold and wet. Good gloves are worth the investment, though.