Long distance moving storage companies?

I am moving 800 miles away (sorry, Brooklyn!) in a few months. What I anticipate doing is packing my car with what I can carry/need, and ideally, have a moving company pick up the rest (which should just be boxes mostly, I'm selling most of my stuff, and no furniture), store it for a few days/weeks, and then when I request it, have them bring it to me within a few days. I've heard of situations like this where you sort of rent out part of a semi, you don't pay for an entire truck yourself, and they drop stuff off along their route. I know that long distance moving is really expensive, and it would not be a lot of stuff, but I don't want to take it with me on my way down, and as I might do a bit of traveling before I settle in, have no clue when I would need it, nor would I have a permanent address yet. So, any ideas would be great! Thanks!