While their upfront price is a bit pricey, plastic storage boxes will last for years and offer more protection for fragile items and protection from moisture, heat, and humidity. They're easy to stack so you can maximize storage space, and open and close easily without having to deal with packing tape. This makes them extra handy for items you expect to need access to. Even if you're only planning on short-term storage when you move, plastic bins may be a good choice for items you'll want organized in your new home in the future.
You can buy boxes made specifically for specific items, such as dinnerware, a flat-screen TV, or clothing. These boxes are great for keeping your items safe from damage as they come with special inserts to secure items for shipping. If you're storing clothes that are best hung, consider getting a wardrobe; it's a tall upright box with built-in bars so you can hang your clothes and the box helps provide some protection, Keep it away from heat and sunlight.
Make sure you can keep track of what's stored with appropriate tags. Trust us, it makes life so much easier whether you're moving or staying put. Most organization and office supply stores have labels that can be easily applied to plastic boxes, or you can use Sharpees to write labels directly on cardboard or plastic boxes. No matter what type of labels you use, be sure to label the sides and top of the bins so that even if the bins or boxes are stacked, you can still read them. It's also a lot easier to label the containers if you have a system for packaging them - they can't all be "miscellaneous" boxes. Group similar items together and try to balance the weights so some boxes aren't too heavy.