"1st class was suggested to us as we will have luggage and we were told that finding seats in 2nd class was a bit of a gong show."
Again, these people have conflated two different things.
If you are traveling on a train requiring reservation (the Frecciarosa, Frecciaargento, Frecciabianco, or InterCity trains), you will have a seat number on each ticket. These tickets do not need to be validated, as they are specific for a particular train number, departure time, and seat. You merely go to your assigned seat; since everyone on the train has an assigned seat, no one should be in your seat (and you can get the conductor's help if they are). So, no "gong show" involved - first class or second class.
If you are traveling on a Regional or Regional Veloce train, these trains neither require nor allow reservations. You do indeed need to validate these tickets before boarding. It is indeed everyone for themselves when it comes to finding seats; if you can't find a seat, you stand until one becomes available. Again, this is true in first class or second class. The catch is, many of these trains have only second class cars. Of course, if you do find a train with no reservations that does have a first class car, it will indeed be less crowded.
I haven't checked your routes to see what's available, but you can do this yourself. Go to the Trenitalia website: http://www.trenitalia.com/tcom-en. Even though it's in English, you need the Italian names of the stations:
Rome: Roma Termini
Florence: Firenze Santa Maria Novella (often abbreviated Firenze SMN)
Venice: Venezia Santa Lucia (abbreviated Venezia SL).
Note that each city has many stations, all with the city name in them. Rome has Roma Termini, Roma Tiburtina, Roma Ostiense, and about 20 others. Don't panic and jump off a train at the first "Roma" one you see (alas, this is a mistake I've made more than once).
For the Cinque Terre, unless you're staying in La Spezia (usually not recommended), put in the name of the actual one of the five towns you are going to or from (Vernazza, Manarola, etc).
For Pompeii, you will go to Naples (station is Napoli Centrale), then change for a local train not operated by Trenitalia to Pompeii Scavi. This local train is the Circumvesuviana; it won't show up on the Trenitalia schedules, but don't worry as it runs 1-2 times an hour and is unreserved and cheap. You just buy your tickets when you get to Naples. Think of it as a city bus on wheels. This one can indeed be a gong show; since you're going for the day, you won't have luggage to worry about.
I know it's overwhelming now; I promise it will be easier once you get there, and have done it a few times.
Ken mentioned it above, but I just want to emphasize that you should buy, as soon as possible, a copy of Rick Steves Italy. It will help tremendously with all of these logistics. For instance, he has step-by-step directions for visiting Pompeii from Rome.