ARM I: Patients receive paclitaxel IV over 3 hours immediately followed by trastuzumab (Herceptin) IV over 30-90 minutes on day 1. Paclitaxel repeats every 3 weeks for 4 courses and trastuzumab (Herceptin) repeats weekly for 10 courses. At 3 weeks following paclitaxel and trastuzumab (Herceptin), patients receive doxorubicin IV and cyclophosphamide IV over 1 hour every 3 weeks for 4 courses. Following chemotherapy, estrogen receptor (ER) positive and/or progesterone receptor (PR) positive patients receive oral tamoxifen twice daily for 5 years.