RR, back to your original question...
If you are IFR on handover, the preceding controller will normally give you the callsign as well as the frequency of the new unit, e.g. "G-XX, Contact East Midlands Radar 134.175", so the question you pose should not arise.
I guess, therefore, that your question relates to a freecall and probably for a service under VFR. I would suggest that, unless you know otherwise (i.e. from hearing a transmission prior to your inital call), your first contact should be addressed according to the service you require. For example, if it is a request for procedural service (such as a VFR join), then use "Approach" or if it is for a radar service (RIS/RAS or Radar Control Service), then "Radar" would be more appropriate.
As was confirmed earlier by
RC and others, I'm sure controllers will not mind which callsign is used to address them on initial contact, as they are usually able to offer either service. However, your choice may just serve as a useful initial indication to them as to which service you may be seeking.
JD
