Depending if you are lifting and pushing the boxes to move or if you're going to have movers do the work, go to your local storage facility and buy a bunch of wardrobe boxes.  The tall ones used for long garments and coats.  They were great for boxed passenger cars and rolling stock and they held a lot.  For your loose buildings, locomotives and cars, wrap them in heavy moving paper and move them yourself if you're not going too far.  If they need to be loaded on a truck, wrap them up and put them in smaller boxes and mark them as a "top load".

For the boxed locomotives, the large plastic tubs with cushioning inside around the boxes will work.  You don't want much bigger than that so they won't be too heavy.  We moved the trains across country this way with no damage.

WARNING

DO NOT ALLOW ANY MOVERS TO PACK YOUR TRAINS.  AND DO NOT ALLOW THEM TO REPACK ANYTHING YOU HAVE PACKED AND ARE HAPPY WITH.

They did that to my stuff, and although nothing was damaged, three years later now I still can't find some of the track pieces.  I had everything packed so I could easily locate everything and when I wasn't looking they took apart some of my packing and combined it with items from other rooms.

Good luck with your move!!  I hope it goes smooth and you're up and running trains again soon!!