The historic center of Florence is tiny. You can walk it north-south or east west in about half an hour.
The very center of town is the north south axis running from the cathedral south across the Ponte Vecchio to the Pitti Palace, and the east-west axis from the Via Tornabuoni to the church of Santa Croce.
I, for one, wouldn't choose to stay in the epicenter, which can be noisy, touristy, and has more than its fair share of tacky places that appeal to some tourists. I would choose to stay a few blocks west of the very center, near the river, on either the north or south side.
Secondly, you absolutely positively do not want a car while you are in Florence. You will not be able to drive it anywhere in the center or park it on the street, and off-street parking is expensive. Read the articles on driving in Florence, on "ZTL rules", and on parking on the right side of this page.
The way to see Florence is on foot. If walking is a problem, there are tiny electric city buses that go all around the very center, and larger buses that will take you elsewhere.
The car will be terrific for going to other towns before or after you have spent your three days in Florence.
As for itineraries, get yourself a good guide book - I recommend the Blue Guide - and come back if you have specific questions.