Staying in Nerano on Amalfi coast - what is best way to get around

To answer just a couple of your questions..;
Yes, you can visit Pompeii en route to Sorrento. You will take a "fast" train to Napoli Centrale and switch to the local Circumvesuviana commuter train at the adjoining Garibaldi station. You'll get off at Pompeii Scavi-Villa dei Misteri station. Check your bags either at the station or at the scavi. When done at the excavation, get on the same train and take it to Sorrento. You'll buy your Circ. tickets at the Naples train station, and they must be validated before boarding.

Here are some good instructions; just ignore the bit about buying tickets to Naples through Italiarail and buy them through Trenitalia or Italotreno.

https://www.seat61.com/places-of-interest/day-trip-to-pompeii.htm

The official website for the excavation; contains LOTS of info including a feel for how vast it is.
http://pompeiisites.org/en/
http://pompeiisites.org/en/pompeii-map/

Here is a current bus schedule for Sorrento>Nerano.
https://www.sitasudtrasporti.it/archivio/Download/corse/sitasud/Campania/Salerno/118f02ca-e661-4469-8401-e65df279297f_5070_11_09_23.pdf/0

Some Path of the gods info from the Sorrento tourism website:
https://www.sorrentoinsider.com/en/e/path-of-the-gods-from-sorrento

..we check out of Nerano. We have to pick up a car (in Amalfi) to head north to
the hill top towns of Assisi and Sienna. We plan to finish our trip in
Florence

You aren't trying to do all of this in one day, are you? WAY too much.
As far as car rental, Sorrento is going to be much closer to you than Amalfi. That said, hopefully someone else can help with the car piece. Worth noting: it's not advised to leave anything you can't afford to lose in an unattended car.

Given the distance from Amalfi to Siena/Assisi, consider taking the train to someplace like Orvieto or Chiusi to pick up the car. The drive would be 5-6 solid hours, so not much time to stop and see things, and the drive from Amalfi to near Salerno will be hell. Taking the bus to Salerno, then a fast train to Orvieto/Chiusi would be much preferred.

I don't really know anything about the Amalfi Coast, but I hadn't heard of Nerano, so I checked the map. I wouldn't describe it as near Praiano. The distance is a bit under 20 miles, but Google estimates the driving time at about an hour; I imagine it could take much longer in June. It's actually closer to Sorrento, though the road looks like nothing but curves. Driving time to Sorrento is estimated at about half an hour (again, possibly a lot longer in June).

Nerano may well be ideal for your purposes, but I wanted to point out that it's rather isolated. I agree that when you get set to leave the area, driving to Amalfi (current driving-time estimate over 1-1/4 hours) is probably not the best way to start.

Is your heart set on Nerano? You're in for a world of frustration no matter the mode of transportation when you stay in these remote areas. The bus schedule says it stops there, but it may only stop occasionally or the stop may be nearby, as in a 30 minute walk away. And don't count on clear signage of where the bus stop is.

As frustrating as the SITA bus system is, having your own car could be even worse. I recommend you research this to death and then reconsider and stay in Sorrento and make your trips from there.

As for a car to Siena; take a train to a closer, more populous place and get your car from there.

Right. Nerano isn't 'near' Praiano. I'll echo the others wondering if you should re-consider a stay at that one; dealing with public transport from there could be frustrating. But having a car wouldn't be any better; getting around the Amalfi Coast during high season is a PITA any way you shake it other than by ferry, maybe. You'd need to stay in villages that have ferry service for that option.

Reconsider the Blue Grotto on Capri too. If there's anything on the island that could be classed as a tourist trap, that's the one. Enough other folks who have done it would also advise choosing other things to do. https://www.tripadvisor.com/Attraction_Review-g488299-d195537-Reviews-Blue_Grotto-Anacapri_Island_of_Capri_Province_of_Naples_Campania.html

We skipped it and have never been sorry. Go for any of the hiking opportunities instead; those will help you avoid the worst of the day-tripping mobs. Ask if you want a few suggestions. As well, although it's an expensive destination, you might consider changing your location from Nerano to Capri for a couple of nights? You can rent kayacks and paddleboards there too. https://caprihydro.com

Google Maps (which is not always precisely accurate, you need to do some SPECIFIC internet research) suggests that the 5070 bus makes the trip Sorrento-Nerano in about 51 minutes. It should be very cheap, but SITA busses tend to be very crowded, so I can't comment about putting luggage underneath the bus. Do note that Rome-Nerano with a stop in Pompeii Scavi is at least a four-seat public transit ride. Do you ever use public transportation at home? ... ... ...

You may also wish to carefully buy (two-three months out) advance discount tickets for the Rome-Naples segment. However, those tickets are sold like air tickets, NO changes, NO refunds, NO choice of a different departure time.

I agree that you have perhaps over-romanticized (or tried for rock bottom costs) a remote place to stay. Transportation is difficult enough in this area even when you stay in a busy, popular, or famous place, like Sorrento or Positano. You are going to be spending hours, literally, getting to one place in a day, and missing some time because of your late arrival there. I can tell you that every one of the five nights we slept at the Ambasciatori Hotel in Sorrento, we saw a long, slow line of cars waiting in line to enter the large underground (paid) parking lot in Sorrento, about half a mile from the downtown restaurant district. You have no idea how supremely difficult it is to have a car in this area between May and September. This is not like going to the Mall Of America with your SUV!

I urge you to read the following discussions carefully:

https://community.ricksteves.com/travel-forum/italy/getting-around-amalfi-coast

https://community.ricksteves.com/travel-forum/italy/one-week-on-the-amalfi-coast

https://community.ricksteves.com/travel-forum/italy/amalfi-coast-for-5-days-where-to-set-base-from

https://community.ricksteves.com/travel-forum/italy/herculaneum-and-pompeii-questions

https://community.ricksteves.com/travel-forum/italy/amalfi-coast-for-7-nights-itinerary-help

https://community.ricksteves.com/travel-forum/italy/naples-to-sorrento-train-or-private-driver

https://community.ricksteves.com/travel-forum/trip-reports/trip-report-2-weeks-of-day-trips-from-sorrento

Thank you for all the great info!!!

I don't see too much noted about the Path of the Gods day, but I did it one day in late April and the FIRST bus we could get (12:30 after the ferry from Salerno) there was a MAD RUSH to it (I believe they added another bus because they expected the large crowd) and I used my Italian "line" skills to manage a seat for me and my friend before it was filled to the brim with standing room only. It took probably 45 min of twisty roads to get to Bomerano, and probably not very fun for the "standers". In June I would be scared of the size of the crowd. I know its expensive, but I would probably arrange for a taxi or private driver to get me up there at a time I preferred. We got up there around 1:15-1:30, grabbed some panini from a shop and headed on the trail. We ended up in Nocelle (the town before the numerous downward stairs to Positano) around 5pm after stopping a few times for snacks/lunch and we gave up on the stairs and took the bus down the mountain to Positano. But I don't know what you would do with your luggage if its on a "travel" day for you.

Sorrento is a transport hub on the Sorrento coast and Amalfi is the one on the Amalfi Coast, so those are your best bets to get on a bus, and if you are getting on ANYWHERE else, you might get passed by the bus if there is no room or you might get squished on with the other passengers, which wouldn't be fun either. If you NEED to stay on both sides of the peninsula, I would make both of those your bases.

My standard recommend, try chatting with Elizabeth at Blue Star ferries in Positano she may be willing and able to help

https://www.bluestarpositano.it/english.htm