An external USB hard drive would work great. Copy your old files onto one then transfer it to the new machine once you have everything installed. They are not too expensive, but maybe a little more than you want to spend. Very handy. If you can't afford one, a USB thumb drive is very inexpensive, but can only hold a couple Gb, so that might take a while depending on how much data you have. I would not be without an external hard drive or a thumb drive, because my main gaming/music computer is not connected to the internet.
While I am definitely for the idea in the long-run (data redundancy is an important thing), it is a horrible idea for the circumstance.
1. USB is much slower than SATA
2. It would mean copying once to the external drive and then once again to the new machine, making any transfer take at least twice as long (ignoring the slowdown due to using USB instead of SATA)
However, as I said, I think the OP should definitely get some backup system in place after the new rig is built.
I live in Wisconsin, it is winter here, I am talking negative 5-20 on a cold day. The parts are coming Via UPS, I am worried about the cold ruining them. I will more than likely be gone when UPS drops the packages off, what type of precautions should I take, I wonder if the boxes will be insulated enough. (Probably not)
http://www.ups.com/content/us/en/shipping/time/service/value_added/hold_pickup.html
Would an electronic heat register work as a ground?
What that is I don't even know. For grounding yourself while working on the rig? A water pipe is your best bet for grounding yourself.