Rome to Amalfi

That sounds like a lovely trip! I am doing a shorter version of that trip (although staying in Positano) and we are going to train to Salerno from Rome and then ferry or SITA bus to Positano (or Amalfi, depending on where we end up renting our apartment). Another option is train from Rome to Naples, then you get on the "local" train from Naples to Sorrento, then bus (and maybe ferry?) to Amalfi.
If you do a search on the Fodors forum, GAC has done an excellent post on this subject.

What town(s) are you planning on staying at in the Amalfi coast?

Right now, I'm considering staying in Atrani, right next to Amalfi.

Hi Jake, actually Naples is the much closer airport. You could fly open jaw (into Rome and home from Naples). To get from Rome to the Amalfi Coast, you can take a train from Rome to Naples (then transfer to a local train to Sorrento) or a bus from Rome direct to Sorrento, 4 hours (both train & bus leave Tiburtina Train Station in Rome). Most people recommend trains over buses in Italy. They are faster and more reliable, or so I am told.
The Amalfi Coast is amazing!

You might look at making Sorrento your home base instead of Atrani, because Sorrento has the easy train connection back to Naples. Atrani/Amalfi does not. Open-jaw is usually the way to go, but I think Naples to Denver is going to involve at least 2 intermediary connections along the way, whereas from Rome I think you can make it with a single connection. You'll have to use a good search engine to check out and price out your options.

One thing to be cautious about is don't attempt making a morning flight out of FCO from Sorrento or Amalfi. Really tough to do. From Amali, you've got the SITA bus and three different ttrains to get to the airport. Of course, theire's the private taxi but it's expensive. We can advise you on train journey times if you wish.

You are all awesome. Thanks for all of the information. I'm heavily considering flying in and out of Rome, just because my wife and I suffer from frequently losing our luggage, so fewer connections are nice.
We'll most likely take the train from Rome to Salerno and a bus from Salerno to Amalfi. We'll probably head back to Rome the day before in order to allow some time.

Ah, shouldn't have mentioned the luggage thing on a Rick Steve's forum! But seriously. Rick Steve's tours take thousands of people overseas each year with just one carry-on bag. I've traveled that way. And I wager, given the various train ferry and bus connections that you'll need to use for your trip, you'd be happy with one carry-on bag too.Take a look at ricks books or onebag.com I've stayed in Sorrento and would recommend it as a great base for your trip. From there it's easy to take the train to Pompeii, the bus down the coast, or the ferry to Capri. Or perhaps split your time between Sorrento and another locale. A small town along the Amalfi coast can be a relaxing destination, but it will be more difficult to visit other locations in the area.