Train from Florence Airport to Piazza Santa Croce

There is only one tram or train from the airport, the T2 tram. You can take it to the end of the line (about a 20 minute ride for 1.50 euros, there's a ticket machine right there on the platform) and walk from there, or perhaps take a taxi if you have lots of heavy bags or limited mobility. If you need a taxi, you can get off at the next to last stop, which is close to the main train station, and find one there. Google "T2 tram Firenze" for more information.

Transport from Florence airport is by tram to SMN station. At the end of the line, walk about a block down via Panzani and catch the C2 bus to via dell Macci. Via dell'Agnolo is the next intersection in front of you. Takes 30 to 45 minutes depending on traffic and transfer timing. If you want to be closer to Piazza Santa Croce, get off at the stop before at Ghibellina Pepi. Via dell'Agnolo is a parallel street one block north.

I think taking a taxi from the airport might be your best choice.
I believe there is a fixed price?
Can anyone confirm this?

T2 to Piazza dell’Unità (basically next to the SMN station) then long walk or taxi (there is a taxi stand in front of the Grand Hotel Baglioni) or C2 electric mini bus.

The taxi from the airport has a fixed fare of approximately 25 euro (varies a couple euros depending if it’s night or day weekday or Sunday/holiday). If you have lots of luggage it might be the more convenient option albeit more expensive since the transit option is only 1.50€per person for 70 min.

Yes, I agree with several of you that a taxi may make more sense with luggage - the Florence streets are rough! What is the best way for me to find the most reliable taxi? They will be queued up at the airport and maybe I can just walk to the front of the line? Should I avoid drivers who approaches me before I get to the front of the line? Will it be clear where to find the line of taxis?

Yes
Just go to the taxi rank out front
Ignore anyone offering a ride before then

It’s a fixed rate to center-I think 22 or 25euros?

Have your address on a piece of paper to give the driver
No tip needed

For the taxi line at the airport, turn right as you exit the building and then right again, round the corner; you will see the line, head to the beginning. The fixed fare to city center is 22 euros plus supplements for baggage (1 euro per piece) and for festive days or night trips.

It was easy to find the first cab in line with your instructions - so THANK YOU! Otherwise, it was confusing because taxis are parked all over the place and it's confusing. I was charged 35E, not 22. I had one bag that he loaded into the trunk and I kept my backpack with me in the backseat. The ride was less than 1/2 hour to Via dell'Agnolo. It was about 13:00 in the afternoon.