Train or Bus?

It depends on the person.

I would take the train back to Zurich airport in one hour and fly direct to Florence otherwise take train with 2 connections that would get you there in about 6 hours.

A flight would be cheaper bought well in advance than taking the train.
You have to look at the schedule on April 2 2020 for the train on this site:
https://www.bahn.de/en/view/index.shtml

I would go with one with 2 connections leavin Luzern around 9. It would go something like this:
Luzern to Arth Goldau
Change
Arth Goldau to Milan
Change
Milan to Florence

The bus would be the cheapest. You can search the bus schedule here
https://www.flixbus.com/bus-routes

If you want to keep it simple, there is a direct train from Luzern to Milan departing Luzern at 12:18. Takes roughly 2.5 hours to Milano Centrale, then you change to a fast train to Firenze. I would chose that over flying for lots of reasons.

Train any day. 5 3/4 hour with hourly departures. There is even one, just after noon with only a single connection in Milan. By air, 1 1/4 hours to Zurich airport, check in 2 hours before flight, 1 hour in the air, 1 hour from landing to get luggage and a tram to central Florence, about the same. Bus? hmm. Highway time similar to the train, but how many stops along the way or bus changes.

If cost is important, check FlixBus fares to Milan and train to Florence. Journey would take about 6 - 7 hours and cost about €50. The super economy tickets won’t be available on Trenitalia until sometime in January.

You can take a train that requires one transfer in Milan taking six hours. Check www.bahn.com.

jr,

I agree with Lola. The train will be a better choice and much more comfortable. You'll have more room to move around, more room to stretch out and there should be food service available. If you use the solution suggested with only one change in Milan, it will also be faster. The segment from Milan to Florence will be via high speed Freccia at up to 300 km/h. No Bus can match that!

Using a flight from Zürich on that route would be absurd. By the time you get to Zürich and go through the usual airport dog & pony show, it won't be nearly as fast. Airlines usually have restrictive and expensive luggage rules to contend with as well.

I wouldn’t use Flixbus if you paid me, having nearly been run off the road by one, whose driver was paying more attention to his mobile phone than the road. Take the train.

train.

Definitely