Have not seen Pontone before but looking on a map online it seems lovely, fantastic views, similar to nearby Ravello I imagine which we did see and thought was magical.
Seems like you could hike down to Atrani or up to Ravello fairly easily ; easier than to Amalfi
The coastal road and roads that snake up to the towns in those hills is not for everyone but I would not have reservations about driving it. Rent as small a car as you can fit your party and luggage in.
The drive is beautiful but twisty, not very wide when cars are coming the other way so requires your full attention and I would try to avoid it after dark.
The main worry is the bus traffic as the buses are fairly wide, so if you happen upon a corner at the same time as a bus coming the other way, it is usually up to you to reverse to a spot where the bus has enough room to make the turn. This could be very stressful especially with a impatient cars behind you but something that is unlikely to actually happen to you.
Some crazy drivers and mainly motorbikes will pass you at all times regardless of your speed but other than those factors it is a nice road that you can enjoy driving as long as your eyes stay on the road and not the amazing view.
You likely need a car to get to your place with your luggage and back. The downside to that car is when you want to visit the different villages, you are going to have a hard time finding and big money paying for parking spots while you visit.
It is much easier to not worry about that and visit places via the bus. October will be slower but still busy in this area and should still be nice weather.
Usually easier to visit Pompeii on way down from Rome, but as stated that makes for one very long travel day if using public transit and if driving you have concern leaving luggage in your car while at Pompeii.
If you have a car it would not be hard to do as a day trip from your base in Pontone
In your case, I would do it that way, the drive is probably 90 minutes max each way which is not bad.
Having a car in this case will be a nice convenience.
My general thought on staying in one of the slightly off the beaten path towns is it makes sense if you are staying for a decent period (5+ nights and want some relaxation away from the crowds) for a shorter stay I think you would much prefer staying in one of the main towns (Positano, Amalfi, Sorrento are the 3 most convenient towns to base in)