'm keen to find out what calls I should make once cleared for the S&G
This does depend on where you do your rating. Southend and Biggin have really long runways and the phraseology I have used / was given / heard on the radio was very very clear. It depended on the circumstances of the landing, and what other traffic there is.
For instance, I was once cleared for a full stop only, and requested to vacate to let the number 2, a A319 land before resuming my circuits.
Usually, I call downwind "G-AB downwind runway xx for Stop & Go" and the clearance given will vary from "G-AB call final, number x" to "G-AB call final, number x, cleared stop and go, backtrack as required".
They're used to having people call for stop and go, especially at night! But always best to chat to them first to make sure!