J.G.
You simple tell him that he has to wake dry three-five nights in a row and then he can wear underpants.
Throw out the pull-ups. I make my kids wear cloth diapers until they are dry. Pull ups give you the sense of being big. I like to keep them in diapers until they are actual big, i.e. able to wear pull on trainers or undies.
As to the bedding. I had double layers...So a waterproof mattress pad and a set of sheets, and then another mattress pad and a set of sheets. I never had to stripe the bed with my son, and only once with my daughter --but she was really sick.
i double up the sheets on the crib too, so it isn't an issue if there is an issue (throwing up, etc.)