I used rubbermaid totes, no damage or breakage. I liked them anyway and tended to use them for storing holiday decoartions, seasonal clothes etc. Plus they hold up better for re-use I find. We'll be re-using the ones I used to move to the UK for a move to Coventry soon in fact.
Make sure if you do use plastic, use the more flexible rubbermaid-type and not the clear plastic sort. I found that the clear ones are more brittle and tend to crack, the rubbermaid-type are more forgiving.