Yes, you'll need boxes, from anywhere you can find them. (Was the 'liquor store' advice borrowed from Mrs. Bitterman? lol) You'll probably also want some packing tape, since most businesses 'break down' (flatten) cardboard boxes so they'll take up less space in the dumpsters.
Lots and lots of ziploc bags can also come in quite handy for the small stuff. They even sell little tiny 'ziploc'-style bags for jewelry and other hobby purposes, and those are great for keeping each accessory to a particular figure separate from each other (so their paint jobs don't rub off on one another) yet still all fit inside a sandwich size baggie.
The original boxes are overrated anyway. I once had a mint Swinetrek arrive in totally trashed condition, because one of the heavier pieces of equipment had pulled its blister free from the cardboard wall, and that had bounced around and broken several small details, even knocked a chair out of the floor. Don't even get me started on the Backstage playset that arrived with a wall broken free, which had broken off doorknobs and all sorts of other pieces.
Bubble wrap, butcher's paper (like professional movers use), gift wrap tissue paper, even the pillow-stuffing material they use for snow in Christmas village displays... any or all of these can work to both cushion the breakable pieces and stuff inside the hollow areas.
Alex