If you Google "mobility scooter rental Naples" (or any other location), there are a number of hits and you can take your choice.
My husband uses one, and it has totally changed our holidays.
As far as we know, they are all rear wheel drive. For a rental, I'm not sure the tyres/wheels are that critical, but pneumatic tyres are a more comfortable ride than solid. Tiny tyres are not good on rough ground. They don't like too steep hills and the smoother the ground, the better. Cobblewtones are fine, for ours, at least.
Consider what car you will rent - we have an SUV and ours folds into the boot.
I'd have a good look at what is available in your local outlets, to see what is available - the range is amazing.
I've just reread your original post. We have taken the sscooter on the train, but folded, and they are not necessarily the lightest luggage!
The other thing to consider is whether or not to buy your own and bring it with you. We just travelled to Budabest with British Airways and H rode the scooter through the airport to the gate. The scooter was waiting at the aircraft door when we arrived. Obviously you would check the arrangements of your chosen airline.
An added advantage that we didn't expect was to be ushered to special lines with virtually no wait.