Most of my clients use PODS or a similar service. A storage container is delivered to your home. You load it up and when finished PODS will pick it up and take it to off site storage. After you have moved into your new home you can have the container delivered there. This saves hiring a truck or movers, and makes it convenient to load up a bunch of stuff.
If you absolutely, positively cannot let it go, get it out of the closets, out of the garage, the basement, and he attic. Put it off-site self-storage or check out one the mobile storage options below. Buyers need to see how big your closets, garage and everything else is. If it is not big enough for your stuff, they sure will not think it is big enough for theirs.