Trenitalia so many options

Kathy, "Non-refundable" means your ticket will be for a specific train. You can't get an earlier or a later train without paying again.
"Refundable" is the same price you pay if you go to the station, and buy a ticket for the next departure.

Are you prepared to commit to an exact date and an exact time? If yes, buy non-refundable and save yourself some €€€.

"in business class or is it first class." - I, along with most on this site, would say 2nd class is perfectly OK, no need to pay more for 1st class.
See this video for the differences: https://www.youtube.com/watch?v=i4DZ-Z_6wjA
And this webpage for lots of info about Italian trains: https://www.seat61.com/Italy-trains.htm

Have you looked in seat61? If not, you may get better info there.

nonrefundable vs refundable

It's really up to you. If you can commit to a specific departure you can save money by using nonrefundable.

If you need flexibility you should choose refundable. E.g. from the airport the day you arrive. A nonrefundable ticket is worthless if you miss the train due to delay or long lines at immigration)

I would try to arrive at the station 30 minutes before departure - and use the time to buy a picnic lunch for the journey.

I almost always buy advance tickets as soon as I know my itinerary. The exception is on an arrival at an airport in Italy. You can never tell if there will be a flight delay. A late arrival could mean forfeiting the ticket and buying a new ticket at full price. Exception to that rule is if the discount is huge and I don't mind adding a couple hour cushion after my arrival time.

If you have never been to the station, and it is a large one, 30 minutes at the most to get bearings, check the departure board, find the right track, and maybe grab an expresso if time allows. If it is a small station with the train arriving from elsewhere and only stopping for a minute to let off and take on passengers, 15 minutes would be fine.

If it is a regionale and the originating station, get there early when the train is spotted on the platform so you can be one of the first people on board to get a seat, because these trains have no reserved seats. Popular routes, like the train from Milano Centrale to Varenna can get very crowded.

Discounted tickets can't be refunded and changes are restricted, but if your plans are set there is no reason to pay more.

On the other hand if you prefer to stay flexible, print out the search results page of your day of travel, get tickets at the counter and be ready to pay the BASE fare. You can't pay more.

The high speed trains are called Freccia-something, but you must check the "duration" column to find the fastest trains.

Nobody except US tourists, businesspersons whose boss does not check the expense report and Italian politicians travel in first class, it's a waste of money, but if you have money to waste... why not? It's nice, but bring your own food.

To make things a little more complicate, note that there are two railway companies: trenitalia and Italotreno. Italo is privateLy owned and runs only high speed trains on few selected routes. Italo's on day fare is called flexi, same as trenitalia: you can't pay more, but you can pay a lot less.

No Dario. In addition to American tourists and Italian politicians, also Italian business travelers use 1st class, particularly those whose tickets are reimbursed by their company. Those few times I’ve use 1st, it was half empty, but mainly people on business suits working on their laptop or making business conference calls. It was like a traveling office.

I've traveled in both classes, and the only difference really is the seat size is a little bigger, and you get a free cup of coffee.
It is a little quieter, as there are generally business people working.
I would definitely book in advance if you know your dates and times.
Saves a bit of money.
When you get to the station prior to boarding, keep a very close eye on the Departure Board.
Sometimes the track and platform is changed at the last minute.

I, along with most on this site, would say 2nd class is perfectly OK,
no need to pay more for 1st class.

Yep, I'm one of the "most" Chris mentions. :O)
The only time we'd book higher than a 2nd-class seat on Trenitalia or Smart on Italotreno would be if a price break on a more expensive tier made the difference in cost negligible. (Editing to add: as Frank posts below that he was able to luck into!!!)

As you had asked about discount codes in another post, price seems to be of concern? Then book the lowest class. Seating is perfectly comfortable; certainly MUCH better than a coach seat on a plane!!!!

What routes are you looking at? The regionales require no prebooking and are plenty fast. If covering long distances prebooking makes sense. I agree with going second class. Am in Italy now and my train from Venice to Ravenna yesterday was fourteen Euros, train travel is generally quite cheap in Italy. Tomorrow I’ll pay twelve Euros to get to Padua. The fast trains that come with seat reservations have a finite number of seats so yes book ahead. Go with no refundable but not on your day of arrival.

vftravels, see OP Kathy's other post for where she's going:

https://community.ricksteves.com/travel-forum/italy/high-speed-trains-45503125-1d17-4fdc-9006-c8fd85e290f1

Don't overlook Italo trains. They're currently offering better discounts than Trenitalia. I just bought a first class ticket on Italo from Florence to Rome for 26.90 euro. I wouldn't usually buy a first class ticket, but is was the same price as a Smart (2nd class) ticket. It happens occasionally.