Venice to Naples

Your best way to go that far would be via fast train through Rome to Naples.
You can buy tickets and make reservations up to 120 days prior to your leaving--at a big price discount.
See: Trenitalia.com

You can't hop on-hop off the fast trains you will need for this, so you would need separate tickets.

Train: It's about 2 hours Venezia to Firenze, which deserves days, not hours, but let's say you take a quick look around for three hours. Add an hour to drop off/pick up your luggage at the station. You can see a few piazze, a church or museum.

Another two hours to Roma, repeat as above, but in a larger historic center, so you will see even less. That's twelve hours and you're not in Napoli yet (1.25 hours from Roma).

Driving would be worse, when trying to park in cities.

Almost anything is possible, but I would not attempt this. Take the fast train directly to Napoli.

Train without any doubts. One of the best connection would be Eurostar leaving Venezia Santa Lucia at 10:25 arriving to Napoli Centrale at 15:35. You will see scenery. It will go by pretty fast.

Train would be much, much faster and less stressful. The full trip by fast train will take 5 to 6 hours. The key cities with fast-train stops along that route are Padua, Verona, Bologna, and Florence [edit: and Rome, of course]. They all have many possibilities for tourists. One of the first three (which are smaller) would probably be better choices than Rome for a stop of just a few hours. Padua and Verona are both very close to Venice. If you have a good bit of time in Venice you could visit one of then on a day-trip from Venice.

Whatever stop you decide on, Google for information about left-luggage options at the train station. There is usually something available, but you need to be sure before you step off the train, burdened with all your luggage.

And I think you will, indeed, need to have two separate train tickets.

There are quite a few direct trains taking only 5 hours (or more that take 5.5 hours with one connection).

I'd also recommend using the high speed trains which travel at up to 300 km/h, as it's the quickest and most efficient method. You'll be able to see scenery from those (although it will flash past the window very quickly). As pointed out earlier, you can't "hop on / hop off" the high speed trains as the tickets have compulsory seat reservations that are specific to time, date and departure time. Make the trip as quickly as possible and use the time saved to see more sights in Naples.

We did this by train this year - it was an easy trip and we enjoyed it. We did the early train - in the 7:00 am hour so as to get to Naples early as we were transiting to Positano.