G'day John,
There are a few different products on the market, most are in the $20 range like Star Brite Water Conditioner, or Tank Cleen. Both available from your friendly local chandler.
My tank was pretty grungy, with some slime on the bottom, so what I did was to fill the tank half way, slosh some Tank Cleen around and then leave it overnight. Drain it into the keel bilge and then because it's supposed to be bio-degradeable and safe for drinking, pumped it out with the bilge pump.
You shouldn't use Chlorine unless you're going to capture the waste into a drum. Even after you've used chlorine, you'll need to rinse it fairly well. Once clean, re-fill and treat with the Star Brite or similar each time you fill up the water and it will be fine.
We also only use the water for cooking, tea and cleaning, never to drink fresh. Although you could at a pinch because it tastes quite OK.
We also have a Jabsco PAR-MAX 1 pressure pump feeding the galley faucet via an inline cartridge filter that we change every 6 months or so. Turn the tap, water comes out
plus, when I get a round tuit, I'll add a deck shower for that lovely fresh water rinse after a summer swim
Unfortunately, I now find the paint/gelcoat is coming off the underside of the cabin sole, so have bits of it floating in the water. Another job, take the floor out and redo the gelcoat in the tank.....
Michael