I moved last year Pix into my old great-grandmother's house (literally one house seperates mine from my grandmother's now) and I had to pack up the whole collection. Not just Sideshow, but the countless other toys ranging from NECA and McFarlane, Hasbro and Mattel, and even my Fisher Price and other childhood toys (don't give that crap away, I loved my dad's old toys and I'm sure when I have children they will love mine too).
Luckily I only moved a few miles and the only casuality was that Der Kinderstod had a small amount of paint rubbed off his nose. Luckily the plastic underneath is the same color and is only visable when closely (very closely) examed.
Best of luck with your move. When in doubt, pack with newspaper and label "Fragile!" Also, it may be a pain to do, but label EVERYTHING you put in a box (on the outside of the box). It makes finding things later so much easier (especially if some of it will be going into storage). I also suggest getting a bunch of zip lock bags and putting any figure's accessories in them (with labels of course) and then tossing them in the moving boxes.