Shipping boxes ahead of time is the way to go. Sometimes one can also get discounts on UPS and FedEx shipping rates.
My advice would be to only pack the things you absolutely need and a few other small things. If you see something big that you like in NY, chances are that it or something similar will be available in Alabama as well. If you forget something, have your family mail/ship it down later when you decide that you might actually need it.
are you planning on moving down by yourself? It’s a lot easier to move down with a family member the first time so you can get a better feel for the area and have a rental car.