Although we recommend you pack with only cardboard moving boxes due to budget, we also understand the effectiveness of plastic bins when used as storage, and you may already have some items stored in them.
If you plan to move belongings in the plastic bins you already own, we suggest you use Bubble wrap and packing paper to cushion delicate items, and also fill excess space in each bin or moving box to prevent things from shifting in transit.
Lastly, make sure the top of the plastic bin is properly taped to the sides, to avoid spilling out of items. Make sure your items are safe when using bins by loading heavy items under light-weight objects.