The best way to operate would be to invest the money and use some part of the earnings to consume allowing the rest to build and earn more. It’s called frugality. Or thrift.
Savings isn’t tax under the FairTax - nor the income from it.There's no free lunch with the Fairtax. The income from your savings is taxed when you spend it...that's the intent of the plan.
Interest earned (savings) or paid (credit card, mortgage, auto loan etc.) is subject to taxation under the Fairtax...as they say "read the bill".