If in a hurry and you are moving things yourself (so you know to be careful) - I suggest the following:

Anything fragile or could chip paint (G1, loose Binaltechs and MPs) - self sealing sandwich baggies along with their accessories. Then all in a cardboard box where they wouldn't be moving around too much. However for Binaltechs and MPs, if you still have their boxes, use them.

BW, CHUG and other similar modern toys that don't have a high breakage or paint chipping risk - Put them all in one of those big plastic zipper bags you can get at the reject shop for like $3. Even if ball jointed limbs and accessories pop off, they would fall within the thick contained bag so not lost.

GPS toys (G1, BW) transport individually within a sealed sandwich baggy using the utmost care. If anything breaks off, it will be contained within the baggy so you can glue back later. Lucky there isn't that many toys that have this condition.