Ryanair
I have flown with them quite a few times, because they operate out of a small airport near to where I live, and are still scandalously cheap (next time I promise I will go by train, but my flights to Madrid to join the Camino in May are one penny each way). They are cheap and cheerful, and (as already has been said) like a bus trip - no seat allocation (first come, first seated), and no frills - but clean and efficient. They charge for checked baggage, so if you can get away with carry-on, then do. They charge for (lousy) food and drinks on board, so bring your own.
They tend to fly into obscure airports, so check where exactly you are going. For example, their Venice flight is actually into Treviso, not Marco Polo - no real problem, except that it is a bit further away, and has a tendency to get fog-bound. They fly into Pisa for Florence (like everyone else). Pisa is a nice, human-scale airport - 10 minutes into Pisa itself, and with a regular shuttle train or bus service to Florence.
I've never had any problem or unavoidable delay with Ryanair - about 8 years ago we had to divert to another airport because of fog, but they provided buses (on a Sunday in Italy!) to get us to our destination.
Just book early online for the best prices.
Best wishes,
Pippa