Looking for advices on ferries from Mykonos to Santorini

BLUE STAR ferries are the "conventional" ferries, that is to say, large (1500 - 1700 psgers, 250-300 vehicles, 4 decks), with large open decks for economy-class seating, thus good for viewing & photos when entering the Caldera of Santorini ... Hellenic Seaways usually "car carrying catamarans" -- which mean a vehicle deck and seating for about 500 passengers, medium in size, quite stable .... SEA JETS, the main part of the fleet, are small, passenger only (about 400+)and in rough water can be rocky, i elieve that Seat jet also owns 2 new large catamarans, CHAMPIONJET 1 & 2 ... bigger, a small back deck for viewing. Other differences:

• LUGGAGE -- when entering BLUE STAR via the vehicle deck, you leave your large bags there, in steel shelving; perfectly safe, you take along your shoulder bag w. all your valuables. On Catamarans, crew takes your big luggage as u enter and shelves it near entry;you take your shoulder bags to seat.
ª SEATING - Blue star is like a small ocean liner, decks passageways, small cafe areas, corridors, get up & walk around. Economy class is 1st come 1st served on deck chairs or seats in cafes; others are reserved seat only, and just indoors.

TICKETS - In september, don't bother to order ahead, just the day before going, stop at any ticket agency & pick up tix.
2-STAGE trip -- When you say "stop at Naxos" does that mean a ferry terminates there & then returns to Mykons or just mean the ferry stops to let off passengers, take on new passengers? In latter case, unless you want to spend 4-5 hours in port town browsig the streets, I would say stay on board. The hassle of getting off then waiting at pier for boat #2 can be tiring & time-consuming.

I am going to basically echo what Janet said.
Absolutely the best views will be on Blue Star. It will be less expensive and slower.

Hellenic and Seajets service this route on large car carrying fast cat ferries. They will be twice the price and get you there twice as fast. They are all stable so no worry about sea sickness unless you are traveling in very rough weather. There is room for up to 1000 walk on passengers on each of these ships. Hellenic has no deck open while at sea. Championjet 1 and 2 have small decks at the side and rear of the ship that are open for you to be outside. They both have a fairly large deck on the upper part of the ship at the rear, its a bit windy at 40 knots though but you can still get good views in the caldera from those decks.

Since it is September the ferries will not be full. I always wait until I arrive on an island and visit a travel agent to buy my ticket on the ferry to my next island. By waiting you retain flexibility. The travel agent will know if there is bad weather coming or if there are any ferry strikes ( this year there is a planned ferry strike Sept 3-5) By waiting to get your ticket you will know what and when the best time to travel will be.
I am pretty sure that one Championjet does the Naxos Santorini run while the other one does Mykonos Santorini.
This image was taken from the back deck on Championjet arriving in Santorini.
https://www.flickr.com/photos/stanbr54/28616454825/in/album-72157671589993576/ if you click the arrow to the right of the picture there are 4 or 5 more images of arriving in Santorini.

Many thanks to Janet and Stanbr for the details and inputs. I’ve learn many good things from you.

By the way, I heard an International Driving Permit is required to operate scooter around town. Is it mandatory?