Yes, there are plenty of plastic tanks available and what you suggest is feasable..
However the simplest setup would be to purchase a couple 50 gal plastice barrels.. These are now fairly common in commercial the food industry and are rated as 'food grade'.. I have purchased them from a retired fellow purchase them from a company that repackages fruit drink concentrate, so they smell like grape or .. juice but are ok for drinking water..
I think I have been paying around 25 to 30 buck for these..
I don't think you would want make this emergency water system anymore complicated than necessary.. No need for a pump, etc. You could set the barrels up on a support so that you could let the water run out of a tap into a bucket. Then you could carry that to flush the toilet a couple times a day.. Carry water to the kitchen for drink and cooking.. Worked fine when I was a kid and we didn't have running water..
You should place the barrel in a location where you can drain and refill them a couple times a year so the water doesn't get stale, if you going to drink it. Therefore, a basement or garage would be a good location.