best way to get from Positano to Rome

The quickest way is to take a shuttle or bus to Sorrento, then Circumvesuviano train to Naples and transfer at Napoli Centrale train station to a high-speed Frecciarosa train to Rome. You can get discounted Frecciarosa tickets buying them online in advance from Italotreno or Trenitalia.

In season you can also take a Travelmar ferry to Salerno and a direct high speed train to Rome. But you should define "best", cheapest? Fastest? Less changes?

PS FrecciarosSa (note the spelling, Rosa means pink whereas Rossa means Red) is the marketing name of Trenitalia's high speed trains. Italotreno runs only high speed trains, so they don't need a brand to distinguish this level of service.

good point, "best" means fastest which is probably a car service but hoping to spend around $100-150 for four vs. $400 that was quoted by a car service, so fastest but reasonable; thank you for the info you shared

Fastest will be ferry to Salerno €14. 70 minutes.

https://www.travelmar.it/_download/orari-travelmar-luglio-2022.jpg

Followed by train €27,90. 1H27m.
Edit: 12:58, train FRE # 8862 premium class.

Train station is a quick 10 minute walk from the ferry.

https://www.trenitalia.com/en.html

Stations … Salerno & Roma Termini.

If the ferry’s aren’t running, bus Positano to Amalfi, change to another bus to Salerno.
This takes much longer.

If you’re sure of your departure date, you can save by purchasing train tickets now. Prices will likely go up as time grows closer.

Note that ferries are subject to occasional weather cancellations. Frecciarossa tickets are much cheaper advance purchase, but then are non-changeable, non-refundable. Are you flying home the same day? Very risky.

Simplest and probably quickest is as above
Ferry to Salerno
Train to Rome

It is also probably the most enjoyable
The ferry ride is great along there, fantastic views

thank you everyone, very helpful
will plan on the ferry/train combo

do you recommend purchasing both tickets in advance or week of, day of? Thank you again
Dann

Have edited my reply above.