SEATING -- YES, if you get the Airplane seating (that's also called REserved Economy-- they cost bout 4€ more than the Economy) you don't have to sit inside at all... you can spend all your time on deck. Frankly, I would not bother with 4 inside seats. Depending on what the "family of 4" consists of, you might want to buy 2 economy & 2 of the reserved-economy... In case there's a fretful child, or if the family includes an elderly person who wants to sit down/lean back/rest ... for most, the deck is the fun part on a sunny day, to watch the wake, and sea gulls and of course the Santorini vista as you enter the caldera. (NOTE: if deck seating is quite full, there are still lots of Economy seating inside at various cafes and along the corridors).
LUGGAGE -- No u don't have to lug your heavy big bags up steps or elevator to the 2nd or 3rd level (economy). Right as u enter the main (vehicle) level, there are steel "warehouse shelves" filled with passengers' luggage. You will of course take with you your smallish day-bags with all valuables, camera, laptop, snacks etc... but your big bags are perfectly OK, perfectly safe on or beside this shelving. TIP: Stack your family's bags vertically, so they won't be buried beneath those of others.
STRATEGY -- The aim of course, is to score good deck seating together or 2 & 2,... a challenge since since it's first-come-first served, it's High Season & pretty full on arrival at Naxos, since its the last stop before the route terminates at Santorini. The strategy will be: (1) Arrive EARLY at Ferry PIer & position your group as close as allowed, behind rope, by BOat Officieals, and when they dropthe rope -- HURRY, it's a crowd scene. (2) Inside, have Paterfamlias deal with the suitcase stacking, while Mama heads upstairs with kiddies or Grandpa, to snare seats -- if kids are speedy Teens send Them ahead to snare & save seats.
ARRIVAL -- the view of Santorini from open deck farries is rightfully praised ... so take time to enjoy... no need to rush down steps, because ferry won't rush away, leaving you on board; this is the terminus; turn-around port.