On the way in, call the handlers (Signature are very good, 123.65) to give them your ETA and find out your parking spot. Also on the way in, you must listen to LHR Arrival ATIS before calling Radar.
Before departure, you must listen to LHR Departure ATIS before calling Clearance Delivery. After that, as stated previously, you get handed to Ground and then Tower. Be prepared for incessant RT; getting a word in is sometimes difficult!
Cost: handling and airport charges currently runnning at c£400 for a A109. Fuel charges have small additions thrown in(bowser and pipeline surcharges) for the privilege of taking fuel at LHR.
That said, it's usually an enjoyable experience!