You need at least 3 nights in Florence, so basically two full days, just to visit the bare minimum sights of Florence (if Florence is in your plans). If you want to take day trips to the Tuscan countryside from Florence you need to add one night for each day trip you intend to make. Having a car in Florence is not needed nor advisable, unless you plan to stay outside the historical city center (which is closed to non residents' cars), so to visit Tuscan towns from Florence you would rely on public transportation (trains & buses) and maybe some organized small tours from Florence (of which there are many from many companies), that is especially advisable if you plan to do some drinking since Italian laws on alcohol while driving are very strict (and country roads are very curvy, so I wouldn't want you to end up in some ditch with your car).
If you plan to split your time between Florence (without a car) and someplace in the country (with a car) then you need several nights at your disposal. As I said Florence needs a minimum of 3 nights, then if you want to stay somewhere else in the country I would want to have at least another 3 nights at my disposal for Tuscany. Visiting small towns is certainly more convenient and efficient with a private car, however be aware that roads and ancient town streets are narrow, therefore a large vehicle like a van, would be more difficult to negotiate those roads and the parking. Also to rent a van costs on average 3 times as much as renting an economy car, therefore if you have a large party, with multiple drivers, it is often cheaper (and easier) to rent a couple of small cars rather than one van. Nowadays even small cars cost a lot (about $350-400 per week).
I don't know what your budget for hotels is, but for a decent 3 star hotel in Florence you need at least 150 euro per room (double occupancy) per night during peak periods, such as Sept/Oct. For a 4 star hotel you are looking at least 200 euro. For hotels I would use booking.com and see what you like. If you are staying for an extended period in Florence (over 3 nights) and/or you have a large family, it might be better to rent an apartment through AirBnB or VRBO. That would probably save you some money.
