¡Bienvenida! a FlyerTalk.
I will move this to the Florida Forum for information on economical services to transfers between Miami International Airport and local hotels. I have also retitled your post, because it appears you are not looking so much for a rental as for a car / limousine (como un remise, ¿no?) to take you to your hotel, and in the Florida forum they would be much better able to answer your question.
I have also deleted your link to a Fort Lauderdale limousine service, as it is not relevant to your question.