Best way to travel from Barcelona to Italy

Yes. Fly. Nonstop and relatively inexpensive

You only have a couple of options ---- plane or train. Use one of the discount airlines. We like easyJet over Ryanair. EJet functions more like Southwest. We have used them several times with good luck. Follow their rules for luggage and you will be fine.

Many options? there may be various methods, like walk, cycle, bus, drive, train, sail, fly but when you look into it the viable options are limited. A bus will get you direct into Italy but usually not the right part, so you need another bus or (better) a fast train. It's a long drive and one way rental will cost a fortune. Trains as far as the Italian border are fragmented, and you still need probably two more in Italy. Then there is the 21 hour ferry crossing to Civitavecchia near Rome, which has terrible reviews especially for cleanliness!!

Which leaves, as already said, fly. Pay attention to condtions and add ons.

How much time do you have to get from Barcelona to someplace in Italy? (Florence?) By plane, it can be a direct flight taking half a day. By Train, 20 plus hours of travel, so you might want to spend a couple nights (or three) along the way. There are also ferries to Italy, to Genoa, or near Rome, still 20 plus hours, but continuous, and you get to sleep in a bed for some of it. But honestly, I would fly before taking the ferry, train would be fine, if you want to plan some stops.

Thank you. I will try Easyjet.
Good to know the ferries are not clean as we had thought about that.