How best to approach the Amalfi coast?

1A. Should I be considering other modes of transportation Venice-Campania or Campania-Rome?
The only other way would be to fly from VCE to NAP but I don't think that it would save you much time and could be more expensive.

1B. Should I consider a slow train rather than the speedy one? (for seeing view, for experience, etc.)
The fast train train is going to take 6-7 hours if you travel from Venice to Salerno. The scenery isn't that great and taking more time for the trip would be a boring mistake.

2A. Naples or Salerno? Or, arrive one, leave the other? And if so, which, when?
I would arrive in Salerno where you could take a ferry or bus to Amalfi which is a good transportation hub to see the Coast. Taxis would be available to get you to your lodgings. You might want to consider a night in Naples just to get a feel for the city and visit the Archaeological Museum. Then leave from Naples for Rome.

2B Arrange for a driver from train in Naples/Salerno and return, or should I consider a ferry in one (or both) directions? Which one is most impressive for views, etc. Ferry is more "back door," but does the inconvenience warrant the experience? See 2A.

2C I have been quoted 120 Euros for a driver from Naples or Salerno to my accommodations just outside Amalfi. Does this sound reasonable? See 2A. I think part of the Amalfi experience is to take a ferry to see the coastline from the sea rather than the sea from the back seat of a taxi.

Oh boy! You pressed all my happy buttons!
1A/B I like the Freccia trains - fast, frequent, comfortable and the air conditioning works. You still see the same stuff!
2A Sorrento for me is a great home base. You can get anywhere from there by boat or by road. From Naples I like taking the ferry across the Bay of Naples - great views, relaxing, fresh air and you avoid the miserable Circumvesuviana train. The ferry going around the coast has the most beautiful views of the cliffs, the beaches, the towns. Hey, you're on vacation so what's the rush!?!
2C I can't speak to that price, I pay 70 euro from my hotel in Sorrento to Naples train station.
3A Again, Pompeii, Capri and the Amalfi Coast (Positano, Amalfi Town) are easy destinations from Sorrento. By car or train to Pompeii; by bus or boat to the Amalfi Coast towns (yes, you can get off and on); and naturally boat to Capri.
3B BOATS! Do some searching and there are very interesting offers out there. One I took with friends a few years ago went from Sorrento, stopped off of Capri where everybody jumped into the water (we're still smiling and talking about that!), took some time in Positano (it seems to me to be all women's shoe stores) and Amalfi Town. Then it repeated the swimming stop on the way back to Sorrento. The bus ride from Sorrento (stand in the very long lines at the train station and don't plan on getting on the first bus to come by) is fun if you are on the right side of the bus, except the people on the left will be leaning over you to see what you see. I like taking the ferry over and the bus back (sit on the left side).
Thanks for reminding me! Time to make my ferry reservations! Remember: You deserve this!

Thanks so much @Ralph and @Robert!

Ralph: Any time I spent in Naples would likely be spent eating pizza! The suggestion of the Archaeological museum is a good one; I'll look into it. I doubt very much though that I would decide to spend a night there because in general I prefer fewer places overnight for longer rather than onesies twosies. I do agree, so much, with your comment that it's better to see the coast from the sea than the sea from a taxi. Yes!

Robert: So glad I could help you get to your happy place! I was not planning to stay in Sorrento but to experience living on the coast, steps and all! I've rented a small house waaaaay up the cliff above Amalfi (town). My week there is less about getting out and "seeing stuff" and more about trying to live as an Amalfian. I was hoping for a slow week, one of espresso in the morning like a local, exploring alley ways, sleeping in the afternoon, dinner with a view. Silly? Misguided? Downright wrong? Any guidance about those boats?

Mille grazie!

My family and I where in Italy last week and we had a wonderful experience using the ferry. Our main destination was Rome but we did stay a night in Salerno. We to the fast train from Rome to Salerno in the morning then got directly on the ferry to Positano. The trip was a little rough but we got to Positano 15 min. faster than expected. We stayed in Positano for the day and then caught the last ferry out back to Salerno. We spent one night in Salerno then got up the next day and saw the city. We then caught the train back to Rome with a brief stay in Naples. We went to Naples to get the pizza. I was not impressed with Naples. A little on the dirty side.

Thanks, @hudgens75!

That sounds like a lovely day(or two) trip.

I'm not visiting Naples, per se; although once I've discovered that the Archaeological Museum has the Farnese Atlas, I've become determined to see it. That, and pizza. And the fast train out of there!

Appreciate your input. Hope your trip was as enjoyable as it sounds.

2C: A quote of 120 euro from Naples train station to your remote Amalfi lodging doesn't sound unreasonable, but that amount sounds high from Salerno train station which is much closer.

My wife and I just visited the area. Flew into Naples, train to Salerno for 4 nights. Used that as a hub.

The ferry to/from Positano (of course, you'd do Amalfi) was (about) 12.50 Euros each.
The train from Naples to Salerno was about 5 Euros
That's 18 Euros each. Pretty cheap. But, then, you have 4 people.

Also, for a day-trip, look into Paestum. It is virtually ignored by average tourists. The ruins of the houses are of low caliber because they weren't hidden by volcanic ash for centuries. BUT you can walk all around / inside them.
Plus, the Greek temples are great.

Thanks @Frank and @Evan,

The financial input is much appreciated!