ive got the same foam gun as the i4detaling in the link.
i however much prefer megs hyper wash as my foam as alot of the others ive tried i dont feel work as well.
if its a dirty car i usually rinse the car with pw.
then foam the car and let it dwell usually 5 mins or so then rinse it off.
then refoam and wash with the tbm.

after the car is waxed etc you get away with simply foaming and rinsing the car as opposed to washing with a mitt.
i usually wash with a mitt once a month or so or when really dirty as the foam is good but doesnt lift 100% everything.