This phase III trial is studying how well combination chemotherapy and radiation therapy work in treating patients with newly diagnosed low-risk rhabdomyosarcoma. Drugs used in chemotherapy, such as vincristine, dactinomycin, and cyclophosphamide, work in different ways to stop tumor cells from dividing so they stop growing or die. Radiation therapy uses high-energy x-rays to damage tumor cells. Combining chemotherapy with radiation therapy may kill more tumor cells. It is not yet known which treatment regimen is more effective in treating low-risk rhabdomyosarcoma.