Aerofoil,
On first contact I suggest you say "Liverpool approach, G-ABCD inbound" -
"Inbound" makes it clear that your destination is Liverpool and therefore what service(s) you require and "approach" shows the controller that you understand the ATC procedures and expect to subsequently talk to tower.
Leave all the rest - where you are, where you've come from etc. - until asked, as others have said.
One thing - if you've been listening on the frequency and it isn't too busy, you might expand slightly to say "inbound from the South" (or N/E/W as appropriate) as it may help the controller co-ordinate your arrival.
SD