Amalfi Coast or Cinque Terre?

I like the CT option because it fits into the rest of your itinerary without needing to travel 3 hours out of your way. The coastline of the Amalfi Coast ( AC) is similar to CT but more crowded. if you’ve seen Big Sur, it won’t be as stunning to you as, let’s say, someone from Kansas or Nebraska who’s never seen Big Sur or even Laguna Beach, Ca.
The other reason for CT is you can start one day in a place like Vernazza and end it in a place like Santa Margherita Ligure or Rapallo- all while passing by Riomaggiore and Portofino! That is a lot of effortless sightseeing by train and boat packed into one fantastic day!
Finally, there will be 14 Cruise Ships docking in Naples from 9/4/25-9/7/25 with more docking at Salerno. You can bet there will be throngs of passengers daytripping to the AC!
Have a great trip!

Under the circumstances, I'd suggest the Cinque Terre this time, primarily for two reasons....

1. Budget - everything tends to be more expensive on the Amalfi Coast.
2. Travel times - getting to Positano especially is going to take longer. There's no rail service there so you'd have to travel to Naples first and then south to Positano, with the last segment being by bus, boat or car service.

In early September, both of those locations will likely still be crowded, especially if there are cruise ships in the area.

Monterosso is a good choice for a location to stay in the Cinque Terre. It's the largest of the five towns and has the best beaches of the five. Note that some sections of the beach are pay-per-use and some are free. Your hotel can tell you which areas to go to.

For the hike on the Sentiero Azzurro between Monterosso and Vernazza, I found that it's easier to start in Monterosso as there's a steep uphill section at the beginning and it's easier to do that going uphill rather than down. Note that a Park Pass is required to hike those trails.

Car rental..... note that each driver will require the compulsory International Driver's Permit for driving in Italy. These are used in conjunction with your home D.L. and can be easily obtained at any AAA office for a small fee. You'll also have to be vigilant to avoid the ZTL (limited traffic) zones that exist in many towns in Italy. Each pass through one will result in hefty fines which you likely won't know about until several months after you return home. Travel by train from La Spezia is not difficult, although there are usually at least two changes on that route. The rail station in Siena is at the bottom of the hill so travellers need to take a bus or taxi up to the town.

You might find it helpful to have a look at the Rick Steves Italy guidebook, as will provide all the specific detail to plan your trip. The new edition will be released in Summer 2025.

Having been to both (easy for me to say), I'd choose neither! Since you are open to renting a car, I would look at somewhere on the Tuscan or Ligurian coast that will not be so crowded (and would have much better beaches for swimming). But, if you have your heart set on one of these, I would definitely choose CT because it maximizes your time much more. Congrats!