If you want to go in chronological order, your tour of the Bargello Museum should start from the first floor, but I suggest immediately going to the large ground floor hall dedicated to monumental 15th-century sculpture, and mainly centered on Michelangelo's marble sculptures from his first early works up to his full ripening.
The exciting Bacchus dominates the room: this is Michelangelo's first monumental sculpture that he made when he was just over twenty years old. Inspired by the elegance and perfect smooth surface of classical sculpture, this work shows how casually young Michelangelo could approach the Greek-Roman models: the god of wine is in a precarious balance and is clearly drunk with wandering eyes, holding a cup that looks like it could fall any second. Behind him you can see a mocking spirit biting into a bunch of grapes. Buonarroti sculpted this statue during his first stay in Rome, and it was for the courtyard of the Palazzo della Cancelleria, in direct comparison with some ancient sculptures. The work made him immediately famous in the eternal city, so much so that shortly after, the Vatican commissioned his first masterpiece, Pietà.
Now shift your attention to the rough Tondo Pitti, a marble version of the brilliant pictorial tondi that were often ordered from Florentine artists during the Renaissance. The figure of the so-called Apollino is ambiguous and elusive, but intimately poetic, perhaps to be interpreted as a sweetened version of David that was left unfinished. Michelangelo's fourth and final work that you can admire in the museum is the energetic bust of Bruto, the hero of freedom, sculpted around the middle of the century at a very delicate moment for the city.
But this hall has other excellent Florentine sculptures in store for you, like the refined Bacchus by Andrea Sansovino, the great bust of Cosimo I made in bronze with virtuous ability by Benvenuto Cellini, and the highly imitated Mercury, an early work by the Flemish sculptor nicknamed Giambologna, where the young god seems to jump into the sky with agility and dynamism. I'd also like to point out the beautiful sculptural groups that decorated the fountains of the Medici villa gardens near Florence.
FUN FACT: under the loggia on the first floor you can see the unusual display of a group of naturally-sized bronze birds, also by Giambologna. Among them I'd like to point out a tattered and realistic turkey, which at the end of the 16th century was still considered an exotic rarity, since it came to Europe only after the discovery of America.