I pretty much never leave anything on the sprue. Mold line clean up is probably one of my favorite parts of building ... clipping a part off the sprue, fondling and close examining it, scraping it free of mold lines down to the basic part ... excuse me for a few minutes ...
I'm back. Everything goes into zip lock bags with LEFT and RIGHT labels as required to keep separate. Tape labels or sharpie marked when the part numbers will be needed for assembly. For painting, round toothpicks, tape, alligator clips ... whatever works for the parts.
I see lots of creative ideas here for holding parts and will be adapting many I'm sure.