Yes. We definitely start with soap and water. And try a couple of times, before we use stronger reagents.
Without knowing what you're working with spazcat: and what your needs are, its hard for us to know what to tell you. 'Tho I'm going to doubt that someone posting in Citizen Chemist needs RCA clean.
In my analytical lab, the first thing I do is use alcohol to wash off the Sharpie writing I've put on the outside of the glassware, so it doesn't end up everywhere. Could this be the source of your "multicolor" problem? Then I use laboratory soap, but dish-washing soap is probably fine for you. I rinse with tap water until the soap is gone. I give it three more tap water rinses, then 3 distilled water rinses. Air dry is usually adequate, but I may oven dry if I need it soon. I don't usually rinse out with solvent, because that's a waste of solvent and a burden to dispose of. However, if you have to do that, acetone is the best choice -- other solvents like methanol or ethanol tend to leave a moisture residue behind.