I consolidate my swap lists for each swap and print out. This contains the group titles, spots I've signed up for (element spots), number in each group, and for the Bazzill swaps I do, the colors assigned for each group. I keep a copy of this at home and in my car. So, when I'm out running errands or between work meetings, I can check the lists in case I need (or want!) to shop.
Then, I pull the embellishments and paper and place in a 12 x 12" heavy plastic craft envelope (can get them at Michaels for a dollar). I also put specific tools, dies, etc that I'm going to use on that group in the envelope if they're small enough. Then, when I'm ready to do that group, just grab the envelope and work on it wherever I want. If I need to cut out some things, I sometimes take that with me and work on it while I'm sitting in traffic jams!! Hey, the light is good!
I label the gallon bags before I get started as well and also print out the individual baggie labels, cut them, and have them ready to stuff in the small baggies for each person.
After I complete a group, I photograph, stuff the individual baggies, add the labels, stuff in the gallon bags and close. Then, I place the completed group in an assembled box.
For swaps that are large and entail a lot of tools and stamps, etc, I will pull all those items and place in a clear plastic container so they're all available for me to pull as I need to for the swap. I did that for the ATC swap which I'm using a lot of stamps and ink.