Is Eurail a good option for training from Venice to Florence to Salerno to Rome? It is within a month so are the 3 ride the way to go? When in Salerno, do you train to the other cities on the Amalfi Coast or is there another option?
There are two major train companies in Italy: Trenitalia and Italo. Trenitalia (Trenitalia.com) is the national railway, and quite comprehensive, whereas Italo (Italotreno.it) is a private company offering fast trains on major routes. Both companies have trains to all of your locations. It’s really better to book with these websites instead of any sort of ‘consolidator’ website.
As for getting around the Amalfi Coast from Salerno, the Travelmar ferries are available April through October. At other times, you would need to use busses or taxis.
From Salerno the towns along Amalfi Coast are connected by ferries and buses, it depends on where you want to go. Eurail is not a good option for Italy. Just buy point to point tickets on Trenitalia.com.
If with Eurail you mean the "Eurail Pass", the no. A pass is complicated to use in Italy, and will usually be a waste of money. Just buy tickets with the operators.
A third party site that may be convenient here is Trainline, as they allow you to compare both operators in Italy. Trainline is even the booking engine behind Italo, one of the operators...
Trenitalia
They also have easy to use app
https://www.trenitalia.com/content/tcom/en.html
No trains on Amalfi coast
Other than local commuter train Circumvesuviana from Naples to Sorrento ( which is not Amalfi Coast)