Your "typical" Western Caribbean cruise, you will be assigned one of the following rotations:
RAERAAE (Royal Palace, Animator's Palette, Enchanted Garden, Royal Palace, etc.)
AERAEER
ERAERRA
As stated above, if you don't have adult dining plans, you are not going to care one way or another. You're going to get three normal rotational dinner menus customized one for each restaurant, and then four special "occasion" menus (i.e. Pirate Menu, Prince and Princess Dinner, Captain's Gala Dinner, See ya' Real Soon) that are the exact same menu no matter which dining location you're sitting in.
I say "typical" Western Caribbean, because those of us with the Star Wars cruises will have Pirate Night on the third night after Cozumel instead of the 4th night after Grand Cayman as is typical.
No one knows for sure how that's going to affect the dining rotations - but at least one person has talked to a concierge or reservations agent who has said that we will NOT be having a pirate menu or fireworks on Pirate Night. So that would mean regular dining menu that night. (You'll still be welcome to wear your pirate attire / costumes to dinner, because there is still a pirate deck party planned for that night). If that is correct, dining rotation assignments will probably still be the same as I've listed above.
Another reason that someone might ask for one rotation over another is that they like the ambiance of one restaurant over another. I myself love Enchanted Garden, but a lot of people find it's crowded and enjoy one of the other restaurants better. As you can see from the rotations on a 7-night cruise, there is one restaurant that is repeated three times, and the other two are twice.
Especially since this sounds like your first
Disney cruise, I wouldn't worry about the dining rotation whatsoever. You don't even know what your "favorite" restaurant will be - and they are each beautiful and unique in their own way. If you start your cruise and decide you don't like the noise of the dining rooms, your tablemates, etc. - there are other options - quick service, buffet most nights, room service. But I think that most people enjoy their main dining experience and also getting to know their wait staff.
I hope you have the time of your life - enjoy it!