European airlines

Assuming you prefer a non-stop flight, your options are extremely limited. I checked a few days in June, and I found only one non-stop flight between those two cities; it's a seasonal flight and I don't think it runs every day. It's on Vueling (Iberia's lower-cost carrier). I didn't find anything to Pisa or Bologna.

You can check connecting-flight options on skyscanner.com.

Airlines vary in their luggage size limits, weight limits and fees, so that can be a decision factor. I've so far succeeded in avoiding RyanAir, a large carrier that pads its bottom line with an egregiously high charge for printing a boarding pass at the airport (if you somehow arrive without one on paper or on your phone) and also has an annoying requirement that non-EU folks find a special desk at the airport to get their passports checked. People have missed flights, looking for that desk. I'm morally opposed to such antics.

I would never avoid a carrier, might prefer one over the other, but most will at least get you from point A to B.

I would start with Skyscanner.com They do a decent job showing you the airlines that fly that route, then you can go to the airlines website to investigate further.

I am seeing flight with Volotea, Vueling, Iberia, and others. There probably are not many direct flights, most look to change in Barcelona or Madrid, but there are a few. If direct is important, you can also look at flying into Pisa or Bologna, then a relatively short train to Florence.

The other thing to remember, is that any European airline, budget or National Carrier, will be much stricter on carry on bags, smaller than in the US, and they will weigh or measure the bag. I find it best just to price in checking a bag when using budget airlines, it is still cheap, and no worries. Do pay attention to requirements, and follow.

If you narrow it down to an airline or two, then I, or others, may have an opinion.

Thank you Acraven and Paul. I was able to find a flight with Iberia ( I called) that is direct on a Vueling.

I was on Vueling once. Got me there. For me thats the only purpose of an airline is to get me from A to B as cheaply and efficiently as possible. Any airline, other than Aeroflop, will work if it meets that requirement.