Ok - where to start
Make life easy for the Controller - Initial call:
"**** radar, G-ABCD, inbound, information ? QNH ****, request (type of service required)".
In this one call you've given him all that he needs to start with. Now, if you've phoned ahead and 'booked in' he'll already have a strip on you - so he won't need half the stuff you'd give him in the 'pass your message' broadcast.
If you've not booked in he'll pick up an arrival strip as opposed to a transit strip and when he says pass your message all you need tell him is type, position, level, point of departure and whether you want to arrive VFR or IFR. That's it - no heading, no request joining instructions, no inside leg measurement. He'll give you clearance to enter the zone, he'll tell you how he wants you to join.
Short - succint and simple and about half as long as the transmission you suggested you were going to make.
In answer to your other question you'll find that the units main radar frequency will be the approach frequency - the two jobs are combined these days and have been at a lot of places for many years. Don't ask for LARS - if they're not a LARS unit then that would be rather silly plus many pilots ask for this without thinking. LARS is just an acronym for a class of service - it is
not an actual type of ATC service - RIS/RAS/FIS (outside CAS) are what people should ask for - even from a LARS unit (I get it all the time - believe me I know
).
Do the above and you'll sound like a pro - enjoy the trip.