. itaiarail or another rail line?

Trenitalia is the national rail company, they run 90% of the trains: http://www.trenitalia.com/tcom-en
Italtreno is a competitor with a few routes only: https://www.italotreno.it/en
Both use the same stations and tracks (for which they are charged tolls, like a toll road).
There are also some local companies (Trenord, Circumvesuviana etc.)

https://www.italiarail.com/ is a ticket seller, which some find easier to use than the Trenitalia site. it IS NOT A RAIL LINE.

should we buy flex fares or set and just make sure we get to the station on time.

Your decision if you want to be held down, your money. Most long distance routes have a train every 60 (some times 30) minutes. Plenty of choice. You do not buy flex tickets for long distance trains, you either buy months in advance, days in advance or turn up at the station and buy a ticket for the next train. In all cases for long distance trains your ticket has a seat number on it.
Go to the Trenitalia site and look up fares for today's trains, and for those in 2 months time, you will see the price difference.

For a full briefing read this: https://www.seat61.com/Italy-trains.htm

I believe you mean Trenitalia, the main Italian train company, or its competitor (on some of the main high speed routes) Italotreno.
You can purchase supereconomy tickets if you purchase far enough in advance. But these come with restrictions. They're nonrefundable and you can't change them. You can buy regular base tickets (full fare) at any time, which are refundable and changeable. There would be little reason other than convenience to buying these in advance.

The type of ticket has nothing to do with your luggage. On European trains, you have to handle your own bags. If they're small enough, they will fit in the overhead racks. DH had a 24" suitcase that fit up there. I had no problem fitting my 22". Anything larger needs to go in the larger racks. These are usually at either end of each compartment. So if your bags are that big, reserve seats at the end of the compartment, if you feel the need to keep your eyes on them.

You can learn just about anything you need to know about European trains here: https://www.seat61.com

I don't think this answers your question, but hope it will help. I often drive in Italy, but I do like to connect the major cities by train. Particularly like Italo (the newer private train line) for connecting Venice, Florence, Rome, and Naples. I'm not sure how far in advance ticket sales open (90-120 days?) but fares are quite good then, even for first class. The only way I think you are going to keep your luggage completely in sight is to put it in the overhead rack. I really prefer to stash mine in the easier racks at the end of the car, and I've never worried about somebody making off with it. The larger problem to me is that there is usually only room in these racks if you're getting on a train that originates at your location. If it arrives from somewhere else, you may have to store yours overhead.

To get to Sorrento will you be connecting in Naples? I don't think the Circumvesuviana train from Naples to Sorrento is going to make you very happy. I would have some concerns about my luggage on that one. The overhead racks are narrow, not really wide enough for much. The one time I took that train it was already crowded, and we stood in the end of the car with our backpacks to the wall and our hands on our roller boards. Especially since there are three of you, consider having a driver meet you at the Naples station and drop you at the door of your hotel in Sorrento. Costs about 100 euro total, and your hotel will arrange it. A very stress free way to start your Amalfi coast vacation! Enjoy your trip!

Italiarail is not a rail line, it is a re-seller.
Two competing companies run high speed and long distance trains from Venezia S. Lucia (Venice islands) to Napoli Centrale (Naples main station): www.trenitalia.com/tcom-en and www.italotreno.it/en. The same trains stop at Firenze SM Novella (Florence) and Roma Termini.

To go From Napoli Centrale to Sorrento you must use a local suburban railway called Curcumvesuviana. They also run a seasonal train to Sorrento called Campania Express: it is faster, comfortable, less crowded and a little more expensive.

No thief really cares about your luggage: there is no market for used clothes and walking inside a station with a big suitcase and a crying tourist in tow is like holding a sign saying "I'm a thief". Pay attention to small things: wallets, mobile phones and all electronic devices, backpacks... those things that a thief can grab and make disappear under his clothes in one second.

On high speed trains you can put middle-sized cases in the space between seats.

If you look on www.trainline.eu, you will see trains by both Trenitalia and Italo. Trainline does not charge any extra fees, but nicely lays out all options with discounts on each route.

Thank everyone. Ok I got it. great now I am set and not worried about luggage. Ciao