Rail from Naples to Florence

First class not that important -at least not to me
We find trains are very comfy in standard seats

All fast trains require seat reservations
Regional trains do not but I doubt you want to travel regional on that route

If you purchase in advance you can get discounts but read the terms as far as refunds/changes

You may find this helpful
https://www.seat61.com/train-travel-in-italy.htm

Both Trenitalia and ItaloTreno run fast trains
Both have easy to use apps

I suspect you are too close in to benefit from advance-purchase discounts, but the Frecciarossa service, which does fill up in summer, and is MUCH faster than other trains, is dramatically cheaper for a non-changeable, non-refundable, one specific departure only, advance purchase ticket. If you arrive early at the Naples station, they will NOT let you get on an earlier train without buying a new, walk-up fare ticket.

I personally try to avoid any transactions of any kind in a busy railroad station during peak tourist season. That's not a rule, just my preference, based on some awful waits for a human agent, behind tourists with no travel savvy, poor command of English or Italian, no working credit cards, and no idea what they need to buy.

A reservation comes automatically when you buy a ticket. 1st class is not that important, but if you buy a nonrefundable ticket early, you might find you can get it for just a little bit more. Check prices and schedule also for Italotreno as they are just as fast, just as comfortable (maybe more), and often less expensive than Trenitalia.

You can buy any train ticket up to 15 minutes before the scheduled departure time either online or at the counter. On high speed trains the ticket will always include a seat reservation, standing is forbidden.

People used to say "only Italian politicians and US tourists travel in 1st class", but Italo's competition and discounted tickets may have changed the things. For sure it isn't "that important", but 1st class is so comfy and calm...

One minor advantage of first class is the 2-1 seating arrangement. If you are a twosome you can get a table on the “one” side just for yourselves, as long as one of you doesn’t mind traveling backwards.

as long as one of you doesn’t mind traveling backwards.

The train will change directions at Termini, so even if you are both facing forward when you leave Nap[les, you will be facing backward when you leave Rome. That is the advantage of seating across a table. Example, my wife hates facing backwards and I don't mind, so we can swap seats when that happens.