"Housing is the biggest budget item in most households,"
Houses are items for sale. New ones are Taxed. Used ones are not.
"Transportation is the next biggest item. Unless you remove the fuel tax, the biggest chunk of that expense is unlikely to be independently taxable"
Gasoline is a new item for sale at retail, so is taxable under the FairTax. Its price, due to being produced in the US, would fall about 20%, and then be taxed up to about what it was before the sales tax is instituted. Its a wash for the fuel buyer. Plus, fuel of the future is electricity, also produced in the US, and would be cheaper due to the removal of income taxes incurred in its production. Consumers, of course, have significantly more money to pay for it with because of the removal of the income taxes, both individual income tax and payroll tax, from their tax burden. Win-win for the US consumer.
"Taxes are the third biggest item. You're not going to charge a sales tax on that."
Correct. Paying taxes is not taxable under the FairTax.
"Utilities are the fourth. Also not a sale."
Utilities are water and electricity, both produced in the US, so the income taxes that are about 22% of their price would be removed due to the abolition of Federal income taxation, and then the FairTax would put the price of each back to about what it was. Again, the consumer would pay with considerable more money than he had before, due to the income taxes being removed from his personal tax burden.
"Food is next. And most attempts at creating a sales tax that isn't heinously regressive do not tax food."
Food is taxed under the FairTax, but the FairTax uses a mechanism called the "Prebate" that sends a US resident all the $$$ he needs to pay the FairTax on subsistence items up to poverty level spending. That is much better than we have now, where the income taxes take the money from the person before he even sets foot in the grocery store. Income taxes tax food, the FairTax does not, at least up to a poverty level. So, the guy existing at low income and eating beans doesn't pay FairTax, but the rich guy eating an expensive plate of truffles is going to bust out of the "poverty level" and his prebate is not going to cover the tax on the truffles, and therefore he pays the FairTax on his rich-living food tastes.
"Health care is next. Also not a sale."
Health care is a service, and taxable under the FairTax. Drugs are new items for sale at retail, and therefore taxable under the FairTax. The dodge here is that you buy health insurance, that is FairTaxed (as it would be taxed by the income tax taking its bite out of your money before you get to the insurance counter and pay for your insurance) and then paying the doctor or buying the drugs is done for you by your insurance, and becomes a busines-to-business transaction, and therefore not retail, and therefore not taxed under the FairTax. Much better than having the income taxes taxing the money you need to either pay insurance or buy drugs and doctor services yourself directly.
"So now what's left at the bottom is entertainment,
Taxable
cash donations to charity (not a sale),
Not taxable
clothing,
Taxable if bought new, not taxable if bought used in a thrift store
services,
Taxable
education (not a sale),
A special category of sale not taxable under the FairTax. It is treated as an investment in yourself. Investments are not taxable under the FairTax.
alcohol and tobacco, and personal care.
All taxable, as they currently are under the income taxes when you pay with your income-taxed salary.