LEGO 75192 UCS Millennium Falcon: I need to store this set, not display it
First, movers are widely varying in quality.  You might get folks that are poets and scholars or you might get somebody that drops every box.  If you've gone with the cheapest movers or this is your first move, it is probably best to assume the worst.  To me this means it is comparable to shipping something through the Post Office.
Given the size of this set it is going to be difficult to get a box that is big enough for it to fit flat.  I would plan on building a plywood box the right size.  If you go with cardboard boxes, get two of different sizes so they can be nested.  Cardboard boxes of adequate width will probably be really tall.  You should cut the vertical corners of the box to make it shorter when the top flaps are folded together.
Then you need to find a material to go between the box and the model.  If you can get foam and cut it to shape that will be easier to deal with, but you could use bubble wrap or packing peanuts.  There's glue for bonding the foam to itself.  I've also used various sizes of towels for packing material around LEGO models.
Particularly if you use packing peanuts, make sure to bag the model before putting it in.  Things that stick out like the radome could get lost, so bag them separately.