Italy has a very good and reliable high speed network, so you can expect the main city to city travel to be good standard.  Local trains (if you are visiting some of the smaller towns) are also generally good in my experience, but be prepared for a lot of stopping, some old trains and graffiti.

Search for “Italian high speed train network map” and you will get an idea of which cities are served by high speed services and which are served by local ones.

I meant to add . . . getting from Rome down the coast to Naples and on to Sicily by train is very much achievable.  You can do it in one trip (like one journey) as there are trains from Rome (and other parts of Italy) which are carried by ferry across to Sicily.  We did a sleeper from Milan to Taormina two years ago and then back to Salerno for a couple of days, flying home from Naples.

There's already a great summary above. :)

Some extra points:

It might not make sense to get a Eurail pass. Advance high-speed train tickets are cheap and regional trains have a fixed (inexpensive) price too.

The only true high-speed part will be Rome - Naples/Salerno.

Definitely do not miss the last European train-ferry over the Messina Strait. For that you have to take an Intercity service. Carriages are detached and shunted onto the ferry.

Trains in Sicily aren't really frequent but you can still get around with a bit of planning.

Appreciate the info . This gets a bit confusing a lot of mixed info, we did this trip 35years ago it seemed so much easier back then,  then again we were in are 20s and didn't worry about anything

What's your thought on how to get from Naples to Sorento, then to Positano then to Tropea then to Sicily all starting in Rome 

The existence of the internet is a double edged sword! 35 years ago, you didn’t need to over plan and over worry. You just turned up at the bus station and looked for timetables pasted up somewhere. If the next bus was in 7 hours, so be it! 

There’s some really good info and suggested routes on Seat61: https://www.seat61.com/train-travel-in-italy.htm 

For mainline train times within Italy, you can just punch the route into the the very well run Italiarail website - italiarail.com. The only trains that won’t cover would be the Naples-Sorrento & back section (it’s only a local railway). And there’s no railway in Positano.

https://www.seat61.com/Italy.htm#london-to-sorrento-and-capri-by-train

Thanks for the feedback , as we look back at old pictures and reminisce about our trip thru Italy and Europe in the summer of 1987, I truly wish we could have spent more time and appreciated what we were really experiencing,

Post cards , pay phones and the “so be it attitude” at a fraction of the cost and headache.

We are just going to keep an open mind and just wing it, we only come this way once in life or in our case twice!!!

Joe