Best Airport to fly into when traveling to Florence within Europe?

From Florence airport into the city is a half-hour bus ride (or taxi). From Pisa airport, there's a short bus ride into Pisa, then a one-hour direct train ride. From Bologna airport is similar, or they mention a private, direct shuttle.

Actually, there's a direct Pisa Airport to Florence bus for 5 Euro with frequent departures; http://www.terravision.eu/airport_transfer/bus-pisa-airport-florencebus/price-and-timetable-pisa-airport-florence/?

You also may find some budget airlines only operate out of Florence or Pisa (not both) so check with the planes you want to fly also

Florence (FLR)
6km (3.5 miles) from the city center, just minutes away. Taxi fare is a flat 20€. Volainbus is 6€.
From Paris (CDG) AirFrance flies to FLR.
From Paris (ORY) Vueling flies to FLR.
Time wise this is the best choice.

Pisa (PSA)
80km (50 miles) from Florence
AirFrance, Easyjet, Ryanair all fly from Paris airports to PSA. Ryanair flies out of Paris (BVA) which is not too close to Paris.
From PSA to Florence you have these choices (in addition to hiring a car or taxi):
1-Directly by bus with two bus companies: Terravision (link given above) or Autostradale (link below)
http://www.autostradale.it/en/
Both depart from the same spot. Trip duration is 70 min.

2-Shuttle bus to train station (8 min) then Trenitalia train to Florence (50 min to 80min depending on train)
Consult Trenitalia website for train schedule.

Bologna (BLQ)
105km (65 miles) from Florence.
Flight choices are the same as to PSA.
From BLQ to Florence there is a direct shuttle bus (90 min). See link below for schedule and prices.
http://www.appenninoshuttle.it
Otherwise you can take the shuttle bus to the Bologna Central station (15 min) then a high speed train to Florence (37 min). The high speed train costs 25€ and up (full base price). See Trenitalia for schedules and prices.

I'd base it on price between Florence and Pisa airports. Take the Florence airport if it is close to cheapest, otherwise Pisa. Pisa is easy to get to and from from Florence.

Check the prices carefully and don't assume that the regular airlines (like AirFrance) will be more expensive than low cost airlines (like EasyJet or Vueling). There are promotional prices and price vary greatly depending on the time of the day you travel.
For example I just checked the flights for a sample date at the end of April from Paris to Florence or Pisa, and the cheapest was with AirFrance, directly to Florence with the last flight of the day. Being flexible with the date helps too. Sometime there is a huge difference between one day and the next.
Also consider that tickets with low cost airlines aren't as cheap as they look after you consider the hidden fees. A checked baggage will often add quite a bit to the cost, even when you prepay online.
Lastly, consider the time too. Flying to PSA or BLQ might be a bit cheaper sometimes, but then you need to add the value of time. If you land in Florence, you are just 10-15 min from your hotel by taxi or bus. If you land in PSA or BLQ, you need to catch public transportation (bus and/or train) if you are not willing to pay 120 euro for a taxi ride from Pisa to Florence (or even more from BLQ). That will add 1 and 1/2 hour to your trip, assuming the bus (and/or the train) is right there when you are ready to go. Sometimes you might have just missed it and have to wait another 30 min until the next one departs.