Sorry for the delay. Life and work got busy.
Our house was built in 1959, and like all homes around here had an underground cistern. Ours is now our storm shelter.
It was built out of cinder blocks under the then attached garage floor and was 20' wide, 26' long and 9' deep. Both front and back gutters tipped slightly (1.5" fall) toward one end of the house so rain would go into a downspout, then into an inverted Y shaped PVC pipe, ending inside the cistern about 1' from the top. That Y pipe had a little lever we'd push to divert the rainwater to an overflow pipe if the cistern was full. Rarely, I mean only in 3-4 very dry summers, did we ever need to have a load of water delivered.
In the floor of the garage was a manhole cover that we'd lift to pour in bleach before a good rain for disinfection. A pump was in the basement on the outside of the cistern wall at the bottom of the steps. We used this as our sole water source for 16 years and would prefer to have it back rather than our current county water. Our water heater was 19 years old before needing to be replaced because the rain water was chemical-free (for the most part) as compared to public water.
You can buy the heavy duty hard plastic tanks and either bury them or put them on top of the ground. You can also dig a large hole and build walls out of cinder block (not recommended) or frame walls and pour solid concrete walls. With time, cinder blocks leak and get shifted due to ground movement but it takes years.
If you tie it all into your house you'll need a backflow prevention device to assure the county/city water doesn't get contaminated. Depending on where you live and local rules, this has to be installed by a licensed plumber and be inspected by the county.
Not one did we have any off-taste or smell, not did anyone ever get the slightest bit I'll from drinking the rainwater. It tasted pure, our pipes and appliances were clean, the water was naturally soft, and was free.
Hope that was of some help.