I use a first wash of hot water with simple washing-up liquid (Ecover) as a run through, then a cold wash with Capritect added (just a slurp to the bucket) and then a final wash with clear cold water. Once a week we clean out the rim under the lid and maybe once a month we dismantle the tubes and all, and soak in Milton. If you cannot get hold of a large container of capritect (Ascott used to sell them , but not sure they still do) Milton will do the same job. I also use a dilute solution of capritect as a teat-dip after milking.
My milking machine has meant that I can continue to have my goats (currently milking 5), as I also have Carpal Tunnel. It is also really the only way for me to sometimes go away, or even just be away for the evening! IMO a necessicity for the 21st Century smalholder!
PS.: My OH carries the hot water for me.... we have a cold tap in the goat shed.