Good idea to try out and sanitize your on board system. As a water system manager, if you are filling with chlorinated city water, there should be no need to 'shock' your system. Contact your water supplier to know for sure the sanitation method and level of sanitizer.
Should you wish, 1 teaspoon of 5% calcium hypochlorite laundry bleach to 10 gallons of water is a 50 ppm concentration. Thats 15 times stronger than pool water. It only takes a couple of ounces, not 1/4 cup. That will kill any fungus, bacteria or pseudomonus. After an hour, drain.
I like to put the bleach in to the fill hose then hook up, so the hose is also sterile.
I keep a spray bottle of dilute bleach in my water bay to spray the camp faucet threads, my hands after dumping.