Train from Rome to Positano

I'd probably opt for Salerno as there are ferries to Positano from there. Your timing would have to work, though. SITA buses also run from Salerno.

There are no direct ferries from Naples to Positano.

https://www.naplesbayferry.com/en/t/salerno/positano

But it depends on how you want to get to Positano? If, say, you opt for a private driver, then I'd probably go to Naples.

I'd do Rome to Salerno.
That is only 1 (or 2 if you take bus). The Circumvesuviana is a crowded hot ride as is the bus from Sorrento to Positano and you can't book that bus in advance- could have a wait as buses tend to be very full.
Plus you'll get to enjoy the views of that end of the coast

Train to Salerno then ferry or bus to Positano
Here is ferry schedule
https://www.positano.com/en/ferry-schedule?from=salerno&to=positano#

Here is bus schedule
https://www.positano.com/en/bus-schedule?timetable_route=salerno_maiori_amalfi
Bus to Amalfi then transfer to bus to Positano

Both the ferry dock and bus stop are just steps from Salerno train station.

If you use a bus to go to Positano and your lodging is at the bottom of town, get off at the first stop coming from Amalfi or the second stop coming from Sorrento. The ferry arrives near the bottom of town. It's a long hike and lots of stairs down from the top of town, or a taxi ride. Different advice if your lodging is at the top of town.