I always bring my basic supplies: trimmer, scissors, lots of adhesives, ruler, pens, etc. I through in a few of my favorite punches.
If I'm going to a store, I bring photos and sketches and then purchases paper and embellies there. If I'm cropping away from a store, then I bring papers and embellies to go with my photos.
Either way, I sometimes hit a stopping point where I cannot continue because I don't have a specific supply. In that case, I finish that layout/project at home and then move on to the next layout/project.