The only things to add is:
1. Get the ATIS before you do anything else.
2. I would vary the first call slightly - it may not be CAP, but it makes your intentions very clear: XXXXX with Charlie, 1016, for a booked landing.
In a few words you have make it clear you have the ATIS and have pre-booked a landing slot - viz via, I know what I am doing, I have 'phoned first and I am hoping / expecting a clearance without any fuss.
(Obvioulsy this only applies to airports of sufficient size and importance that you cant just pitch up without having pre-booked - Manston is a good example with their acres of unused tarmac
, but Gatwick would do equally as well)