10 day Itinerary starting and ending in Rome, heading South

With 10 days, you could arrive into Rome, train directly from there down south. With 10 days, and only wanting one region, Campania, you could break it up and do a stay in Naples (to do the archeological museum and various sites and some ruins or two) a stay in Capri to explore and enjoy without the day trippers, and then a stay on the Amalfi Coast (to do Ravello, the Path of the Gods, tinier towns). You could replace Capri with Sorrento and do one (or more) of the ruins and a visit to Capri from there also, but I will leave the Sorrento/Capri/Naples experts to weigh in on that. You would then leave Amalfi by ferry (hopefully) to Salerno and be in Rome the night before your flight with a stroll around the historic center to cap of your Italian adventure.

If you wanted to stay in Salerno or do a longer day from Amalfi, Paestum, some of the most well preserved Greek temples outside of Greece is easily done :)

You're in luck, there are almost daily posts here regarding your plans. You have a wealth of info ready to access.
Review the posts under Italy.
Review Trip Reports.
Review the RS suggested route in the Guidebook.
Reviews the route RS uses in his tour.
Check the related articles on the "Watch, Read, Listen" section here.
Join area- specific Facebook groups which are especially good for real- time info.
Be aware of the infrastructure issues in the AC, and that moving about is time- consuming and frustrating, with poor public transportation.
Once you've done your homework, and narrowed your interests, we can best help with specific questions.
Also, you're a bit late to be booking accommodations in these areas, so research what's available.
That being said, you have all the tools for a great trip. Safe travels!

We stayed in Sorrento and visit ed Naples and Pompeii from there. The Circumvesuviana train makes it easy. In addition to the Pompeii site itself, be sure to visit the National Archaeological Museum in Naples, with most of the items recovered from Pompeii. There’s also Herculaneum, another ancient city buried in the same eruption as Pompeii, but it’s different, and there are surviving buildings in better condition than what’s left in Pompeii. Seeing both is recommended, if you can include them in your itinerary.

As Pat said, there is a lot of information on the RS website, also YouTube. I can't tell if you've been to Italy before. Here are a few links you can start with
Explore Italy https://www.ricksteves.com/europe/italy
RS Italy guide books https://store.ricksteves.com/shop/guidebooks/italy
Forum posts using search feature for the past year https://search.ricksteves.com/?button=&date_range=1y&filter=Travel+Forum&query=italy+travel&utf8=%E2%9C%93
RS Europe PBS shows https://www.ricksteves.com/watch-read-listen/video/tv-show

You've somewhat narrowed your interests down to Rome, Naples, Amalfi and Pompeii. Make a rough itinerary per day. Decide where you want to stay and for how many nights each. Remember that every time you change locations, you are using at least half a day. Use a map to help lay out your travel so you don't go back and forth. As I plan my days' itineraries, I use my phone's calendar so I don't over plan, have time for meals and transportation, and time for the all-in-important gelato.

As you start to refine your travel plans, ask questions, and clarify. You need to get busy planning. The one thing I would NOT do is rent a car and drive between your towns. The trains work perfectly fine.
I've been working on my September trip itinerary since last August, booked flights in October, hotels in November, and am booking museums now as my days open.

EDIT: Cyn mentioned the National Archaeological Museum. I would visit it after going to Pompeii. It puts the NAM exhibits into perspective.

We are interested in Pompeii, Naples, Amalfi Coast, and other scenic
areas. Looking for travel itinerary highlighting these areas. We have
10 days not counting our travelling to and from US.

Do you want to spend any nights in Rome other than the night before your departure?

We are headed to Rome tomorrow from the US, we are staying in Rome 5 nights, 4 nights in positano and 2nights in Naples. We are flying into Rome and out of Naples.that way you don’t waste too much time in transit

doing about the same thing starting next week. 3 days in Rome (spanish steps, trevi fountain, pantheon, travestere neighborhood first day, vatican/sistine/s peters next day with colosseum, forum, palatine hill last day). enough cushion in that schedule to do other stuff/relax/drink in Rome. Next day, take train to Naples, visit archelogical museum there and explore other sights, visit pompeii the next day. Renting a car to drive to Sorrento where we are staying for 4 days. Dont need a car depending on where you are staying but our airbnb oversees the water and is 20 minutes from sorrento so i traded for the view.
Taking ferry ride to capri and positano for day trips on two of those days with rest of time to relax/explore sorrento. taking train back to rome after driving back to naples and flying out of rome next morning.

I found the co-pilot feature of bing.com helpful in suggesting itineraries/places to see etc.

Thanks for the great tips and itinerary suggestions! It seems I’m on the right track!

Hey there, yes you're definitely on the right track. I'm not sure if you've been to Italy before, but Rome is a bit less chaotic than Naples, so perhaps start there, with jet lag get settled in before heading down to a more hectic city. Where are you staying on the AC? Personally, I would choose Amalfi, large enough to wander, bus up to Ravello, take the ferry along the coast rather than buses, god forbid. Positano is best viewed from the water, no need to day trip there. OR - Others recommend staying in Salerno, good beach and a real town with good food, you can access the AC via ferries from there. Also use search bar above, just type in something like, 'Salerno Forum'.

If you haven't booked your flights yet, you could consider a multi-leg, into Rome & out of Naples, no back tracking. I loved Capri & have been 3x, but haven't been there in decades, lots on the forum using the search bar above about how to spend at least a day there, frankly staying a few nights would give you a better feel and be quieter in the evenings. As others have mentioned, do see the Archaeological museum in Naples! I still recall the awe and wonder of it's statues, long before i was interested in ancient Roman & Greek art. It will help make your visit to Pompeii come alive.

If interested in a deeper dive into Pompeii, watch Pompeii, The New Dig on YouTube. Before our Dec trip to Rome, I got much more interested and immersed in ancient history & archaeology, it really made a difference!