It's a top down service, so you would want to contact someone in the same order as you described in your first post. However, you may be flying into what we call uncontrolled fields, which will only receive approach services. The best thing to do in this situation is to either read the ARTCC's website, or simply ask the controller when you are online. You would only need to ask APP/DEP or CTR, since tower will only control at the airport specified in their callsign.