Which Medici palace in Florence

Palazzo Medici-Riccardi. I don't remember what they had in terms of clothes, but that is the Palace where they lived.

If you have time, visit also Villa Della Pietraia, at the Castello district (on the hill just north of the airport). There are many other Medici's villas, but that one is the closest.

Also consider the Palazzo Davanzati. Although not a Medici palace, it was the home of a very wealthy family and I recall getting a better sense of how families (wealthy ones!) and those who served them, lived during the Renaissance than I did in any of the Medici residences. Many pictures online.

Not sure how your request can be managed. Palazzo Medici-Riccardi was built by the first, really important Medici generations, it was where they lived, but half of the venue is now taken by the prefecture offices, what is left are a few important art works, a garden in a courtyard, and some collections mainly from the Riccardi family that subsequently owned the palace.
The last Medici generations lived at Palazzo Pitti, but what is left there is their immense art collection (but for the very best pieces at Uffizi), and the room settings reflect just their very last generation, the Lorraine setting and even the Savoia setting when the venue was Italy's royal palace in the middle of 19th century. You may be interested in some of the minor collections at Pitti: the museo degli argenti houses the Medici jewel collection, and I remember once seeing at museo del costume an original burial dress for some major female member of the family, that was literally taken out of the tomb and painstakingly restored; but I cannot rememeber if it belonged to the long term exhibition or to a temporary show. But I do not remember an original Medici setting anywhere.
Palazzo Davanzati is an early 20th century reconstruction of a 14th century aristocratic home, so while it is not original, it may give a good idea of an original Medici setting.

Regarding the Ptti: the Imperial and Royal Apartments and Museum of Costume and Fashion are all currently closed.

https://www.uffizi.it/en/pitti-palace/costume-and-fashion-museum
https://www.uffizi.it/en/pitti-palace/royal-apartments

Another vote for Palazzo Davanzati.
It’s huge inside, with many amazing details.
Definitely a “how they lived back then” experience.
If you get there at the right time, you’ll join a free guided tour.
No need for advance tickets.
It’s right in the centre of historical Florence on Via Porta Rossa.