Sicily to Naples / Amalfi Coast by train or ferry

I heartily dis-recommend the overnight train. I took that train in 2015 from Rome to Catania, and it was a miserable experience. It jerked from side to side constantly, and I was unable to fall asleep. That was not too much of a problem on earlier night trains (admittedly, I was much younger then), so I think it's an issue with the rails. They are just not smooth enough for an overnight train trip.

While I like both Palermo and Catania, they are two large, bustling cities. I hope you'll have time while in Sicily to see some other places as well.

I don't think that your direction of visiting really affects the decision of the long-distance transport. I'm sure that you'll sleep better on the overnight ferry to Naples. These large boats are not particularly weather dependent and private rooms are quiet and comfortable. You can also usually fly quite affordably (try www.skyscanner.com).

Naples train station does store luggage.

If you want to fly from Sicily to Naples (that's what I'd do), do look at all the airline options. Note that Alitalia has a more generous carryon allowance as well as one free checked bag, so it can be cheaper in the end than the "budget" carriers on these routes. For Alitalia domestic flights like these, their International website has an English language option and the same prices as the Italian website which is in Italian only. https://www.alitalia.com/en_en/ Their US website often has much higher prices - for the exact same flights!

Note that while Palermo is a bigger city, Catania is the bigger airport, with more options. And these flights can get substantially more expensive closer to travel, so if you do want to fly, buy the tickets as soon as you're sure of your plans.

I agree with acraven - I hope you're spending enough time in Sicily to see other places besides Palermo (which I really liked) and Catania (which I didn't get to). In particular, Taormina is magic, and then there's Noto, Ragusa, Siracusa, the Villa Romana near Piazza Armerina...

Other have covered the transport from Sicily to the Amalfi Coast, but I think you may have a misunderstanding about the hiking aspect of your trip. Direction won't matter much--most people pick one or two bases (depending on personal preference and which day trips one wishes to do), and to access the hikes, you can use public transport to assist in reaching trail heads. There are two books devoted to the hikes, one published by Cicerone and the other by Sunflower, and I recommend picking up one (tourist office can provide info too, but I liked knowing in advance since transport is so important in the area).

Thanks all for your advice! I think we will opt for the ferry to Naples. Arriving on the waterfront at an early hour of the morning seems more appealing than flying or by train.

Does anyone have an opinion on which ferry to take - SNAV, Tirrenia, anything else?

As for the advice to spend more time in Sicily, we are definitely planning to visit again, now that Norwegian Airlines fly from Seattle to Catania.