Here's what worked for me.  Basically got the procedure from an RV book.

My water tank hadn't been used in a while when I bought the Westie so I first
cleaned a bit of crud out of the bottom of the tank accessing through the big
tank lid inside under that little sheet metal cover.(Leaving this lid off
makes tank filling a snap, BTW) Then I filled the tank about 1/2 full and
added 1/4 cup of Clorox bleach then finished filling the tank.  I then ran the
sink faucet for awhile until I smelled the bleach smell coming out.  Drove
around for an hour on errands and let the bleach sit for another couple of
hours.  Drained the tank using the faucet and pulling the cap on the bottom of
the tank.  To remove the chlorine taste and smell I refilled the tank with
water adding to it a big cup of water (Super Big Gulp size) in which I had
dissolved two heaping tablespoons of baking soda.  This I also ran through the
faucet until I felt the slippery water come out.  I left this mix in and drove
around some till the next day.  Drained this mix and flushed with a final tank
of clean water so no white crusties formed from the baking soda residue.  Tank
was then sparkling clean and hygienic.  After a week camping at a place that
had kind of rusty brackish water there was a bit of brown residue in the tank
again  so I just went through the whole procedure again and it cleaned right
up ready for the next trip.

A bit time consuming but cheap!

Good luck,

Carl
84 and 85 Westies