Don't you dare buy boxes.
I can't believe the number of people who buy boxes. WHAT!!!
Boxes are not at all hard to come buy and it is a waste of money to purchase them. Places to get boxes you ask? Easy, many business are dying to get ride of their boxes. Recycling costs money as is paid by volume. If you minimize the volume, well done business owner! So...simple places to grab boxes: outside liquor stores, grocery stores, Costco, and on Craiglist. Craigslist can be a great place but might not be as valuable in other areas in the US. I live in the extremely Eco-Centric Pacific Northwest and upcycling boxes might be more common up here.
Secondly, as you start to pack your things and make plans for your new place start making a list of thing you will need to purchase. Since you are hopefully taking my advice and packing early, this will give you time to pick up the additional items you will need and buy them at a good price. For example, we have recently broken quite a few of our drinking glasses. I have those on my list. I like to purchase those kinds of items at the Dollar Store. They are of course cheap and last a long time. However, when I get into my new place, I don't know the area so well. I don't know where all the stores that I like to frequent are and I might find that I buy new glasses at a higher rate somewhere I wouldn't have intended to buy them. Make sense? In addition, this will prevent you from over purchasing on impulse items when you get into your new spot. If you are like me you get excited about decorating and settling in as soon as possible. If you have to purchase new curtain rods, you might find temptation to buy more and more things while making a quick run to Target. So, as I stress always, make a pre-plan.
Another quick and easy-ish way to get ride of old junk is to take it to a recycle center. If you are moving a garage, I am sorry, it can completely suck. Garages are a place that get filled with junk. Go through you things and if you don't know what it is :) don't use it, or can't think of the realistic scenario when you would use it, recycle or give it away. The great thing about taking old junk to the recycle center they will either recycle it and/or you might get a little cash for it.
Old metals of various kinds lead to quick cash. Consider what is more realistic: need $40 or finding some way to use broken down plumbing parts????