Rome FCO to Florence

I would take the train
Drops you right in historic center of Florence rather than out at airport

There is usually one direct from FCO at 1:53 pm
Trenitalia
Sept schedule should be up June 11-12
Don’t buy tix in advance in case of delay

You will only go thru passport control once on your arrival to Rome

Yes thru security for the second flight if you decide to fly -leave a good buffer between flights
2 hours? More?

...is it correct that Trenitalia and .Italia post their schedules 120 days?

Just look at the same day of the week that you'll be arriving in the next week or two for departures from Termini - the schedule won't change much at all, and departures are so frequent that you can just arrive and buy a ticket for the next train.

Assuming you fly non stop with WestJet from Calgary YYC to Rome FCO, your flight will arrive to FCO at 12:40.
I don't think WestJet has a codeshare agreement with ITA, so you might need two separate tickets, which requires extra time for the connection in Rome.

In any case, ITA only has 4 flights a day from FCO to FLR. The one departing at 13:50 doesn't give you enough time for the connection, therefore you'd need to wait until 17:20 for the next flight. That flight arrives to FLR at 18:15 and from there you can take a light rail tramway to the city center or a taxi . In the best of circumstances you can be at your hotel downtown at 19:15.

If you arrive at 12:40 in Rome, you could catch the 13:53 train at FCO station (no change required at Roma Termini) or maybe a train later (there is at least one every 30 min) and be in Florence 2h20 min later, before the 17:20 ITA flight even departs, therefore I'd opt for the train.

Regarding trains, I know you might get a discounted ticket if you purchase in advance, but discounted tickets come with restrictions (they are not refundable, and they are changeable only in limited situations), therefore it's risky as your flight might arrive late or even be canceled. I'd purchase the ticket and pay full price upon arrival at the FCO station. Seats don't sell out, and the about 30 euro maximum saving may not be worth the risk.

Wow. Thanks everyone for this info. So helpful. I had no idea the trains could be accessed from Rome airport.

Just to clarify
There is only one direct train a day from FCO to Florence 1:53 pm
For all others you take the Leonardo Express to Termini where there are multiple trains every hour

Yes. Understood there's only the 1 train at that time from FCO. Thank you.