I put dried lavender in with anything made from fabric to help keep bugs away.
If you are concerned that things could get wet (eg roof leak). Then put garbage bags if putting into cardboard boxes.
If using tubs, go good quality, especially if stacking on each other. Those lids can crack and the mice get in (I lost 7 metres of silk to mice )

Remember to either write on boxes/tubs or log in a document. I track in a spreadsheet, box number and what is in it. Not just generic, but some reasonable details. Make is easy when you want to find something in particular. You don't want to search through 3 boxes of clothes, when you can go straight to the box with the winter jackets.