I've only used Uber to get to Port Everglades from a hotel so can't speak on disembarkation and such, but there are going to be a lot of drivers looking for fares so you should be able to get one willing to go to MIA.
I've used the bus to get to MIA. Relatively short ride, but you're stuck waiting until it fills up before it goes.
Car service would likely cost more than uber/lyft but you have a little more control over what kind of car will be transporting you.