Your options are Verizon, Tricom-Telecable and Faster, by Aster. You can choose between a modem dial-up connection or a DSL or a cable conection. Any case you'll be charged a monthly fee, no matter how many times you connect, or how long you stay connected. I think that if you use a phone line of one company (verizon or tricom) and have an internet dial-up connection with that same company, you are not charged the minutes you use your phone line (servicio local medido- local timed service perhaps?).
for more information try to visit the websites of these Internet Service Providers.