Staying in Florence for first time

Florence is very compact.
Stay in the historical center or consider the Oltrarno- across the river. You'll be able to walk to everywhere from either.
No need at all for a car, would just be an expensive headache.

Oltrarno gets my vote; most of the hotels are closer to the Duomo, but the apartment rentals are great in the quieter Oltrarno area. It is a very compact city, so walking across the river is easy.

Since it's your first trip, two pieces of information. First, street addresses are either red or black, with an amazing potential for confusion in the congested center. Second, no one will tell you this, but Trattoria Mario near the Mercato Centrale is a hidden treasure for lunch. It is impossible to find, but persevere--it is worth the trouble. It appears they now take reservations, which would be a good idea. Don't tell anyone else about this place. It's just our little secret.

On several visits, i’ve always stayed in the Oltrarno neighborhood, just west - across the Arno river from the main historic center. Since you’re staying about a week, look into renting an apartment there. The neighborhood’s just a short walk across a bridge to get to major sights in the city, but has sights of its own, and will have convenient restaurants, plus shops for picking up groceries and any other supplies for fixing breakfast and other meals in your apartment.

As noted above, a car isn’t necessary - in fact, it’ll be a liability. Unless you’re driving to day trip destinations outside of the city, a car won’t help. The outlying day trips can be done by train, and trying to drive in the city, especially where there are ZTL (zone traffic limitation) areas where you’ll get hefty fines for even accidentally driving into one, save yourself the hassles and avoid having a rental car. If you’re going elsewhere in Italy and want a car, get it after you’re finished with Florence, and/or drop off the car before you start your Florence week.

Another vote for Oltrarno area. We enjoyed staying at Hotel Silla. Great location to sites and restaurants. We were there for 3 nights at the beginning of a culinary tour throughout Tuscany & Umbria. As mentioned, no need for a car in Florence. We walked everywhere from our hotel. Enjoy your planning.
https://www.hotelsilla.it/

Ck out Palazzo San Niccolo apartments. Lovely in Oltrarno..

Another vote for the Oltrarno area, across the river from the centre where the Duomo, Uffizi, etc are located.
Also look at staying just beyond the Piazza San Marco, it's quiet there too.
This is where we stayed last trip.
It's a little expensive, but there were four of us sharing.
It was probably the absolute best apartment I've ever rented in Europe in 20 + years of renting.

https://www.airbnb.ca/rooms/9306481?
sourceimpressionid=p316335435087uWIhPbqYzqQRZO1&guests=2&adults=2&checkin=2022-06-20&checkout=2022-06-27

Still easy to walk into the centre from there.
There is no need for a car in Florence...it's too easy to park in or drive into a Zone that you will subsequently get fined for being in.
There are little electric buses that go all around the areas you will want to see if you get tired of walking.
I hope you will love Florence as much as many of us here do!