Ciao!
To be honest, if you're based in Prato, the best method to get into Florence for a day trip and avoid traffic and parking fees is to catch the train directly into Florence's Santa Maria Novella.
All the roads to Florence are congested with traffic into Florence in the mornings, so you'll make better use of your time if you take the train -- it is about a 30 min ride and costs 2.60 euro one way. You can just get tickets the day of.