The best thing is definitely to park right outside Florence’s center, in Scandicci, that is connected to Florence Santa Maria Novella train station (city center) with the tram.
On Via del Sansovino in Scandicci is the nearest parking lot to Florence. The tram stop, called “Sansovino” is right in front of the parking. Though a paid parking, it is far more cheaper than the parking at Florence’s station.
Let me know if you need any other help,