One day
If you only have one day, do not try to do the museums.
Start at the dome — you booked the climb before anything else, because it is the only part that must be reserved. Come down into the cathedral, which is free, then the Baptistery doors from the square.
Walk south to Piazza della Signoria for the free sculpture under the Loggia, past the Uffizi courtyard, and over the Ponte Vecchio.
⭐ Then keep going. Cross into the Oltrarno, eat there, and climb to Piazzale Michelangelo and San Miniato for the end of the day. That is a complete day and it costs almost nothing beyond the dome.
Two days
Add one big museum, and the other bank properly.
Day one as above. On day two take the Uffizi or the Accademia — not both, and not on a Monday, when nearly everything closes.
Spend the afternoon across the river: the Brancacci Chapel, Santo Spirito, and the workshops in San Frediano.
⭐ If the Accademia is sold out, go to the Bargello instead. It is the better sculpture museum and a fraction as busy.
Three days
Now you can afford the churches, which is where the paintings actually are.
Days one and two as above. Day three is Santa Croce for Giotto and the Pazzi Chapel, then San Marco for Fra Angelico's cells — which is the single most under-visited great sight in the city.
Fit in the Medici Chapels and the Museo dell'Opera, which explains the dome you climbed on day one.
⭐ Three days is the first length at which Florence stops feeling like a queue.
Five days
Two of them should leave the city.
Three days as above, then Palazzo Pitti with Boboli and Bardini — a full day, and do not attach it to the Uffizi.
Take a day out to Siena or Lucca. Both are comfortable returns and both are better than a fourth museum.
⭐ Keep Fiesole in reserve for an afternoon when the centre becomes too much. It is a city bus.
A week
Enough to go slowly, and to reach the coast.
Everything above, unhurried, with mornings for the booked things and afternoons for whatever is nearby and open.
Two or three day trips: Pisa is half a day, Arezzo is quiet and easy, and the Cinque Terre is a long day that is much better as an overnight.
⭐ At a week you can start eating properly — markets in the morning, lunch in a working trattoria, and the steak ordered for the table.