Your best bet is actually to take one of the vans that run out of the station. It's about half the price of the taxi. They are all licensed guys who run through one company, at least the ones I use. They even have permission to pull right up to the Amtrak station, which the taxi drivers are not allowed to do. Here's the contact information, if you're interested:
Florida Van Pools, Inc.
407-414-6006
They will schedule a time to pick you up based on the train schedule. Every driver we have had through them has been extremely friendly and helpful and they get you to your resort very quickly.