I would recommend you to book a flight from Lamezia Terme airport (which is close to Vibo) to Pisa which is a nearby town to Florence (www.ryanair.com).
Or either you can take the train but there is no direct train from Vibo to Florence...it means that you have to change train (I am sure in Rome or Naples). Taking the High Speed train it takes about 4 hours to get into Rome (65€), with the normal second class train it takes around 5hr. Then from Rome to Florence by taking the High Speed train it takes 1 and half hr ( 44€)...with the normal train it takes 3/4 hours (around 20€).
More or less by train or car it takes the same time...with the High Speed train you can travel confortable, but you have to consider the train connection (in Rome or maybe Naples).
If I was you I would probably fly from Lamezia to Pisa and then rent a car in Pisa...the flights are usually cheap with ryanair.
If you need anything else related to this let me know