A flat "resident" tax would obviously be the most fair. Everyone has equal rights to the roads, the firefighters, the libraries, etc so simply divide the budget by number of people and everyone pays their fair share.
Obviously that wouldn't be tolerable in contemporary America, but there is still something absurd about suggesting that because some houses in my neighborhood sold for more last year, that I should have to pay thousands of dollars more for the local government.
The massive inflation in city and state budgets due to soaring property taxes is a huge abuse of the middle class and transfer of wealth to the pork barrel of connected insiders profiting from government contracts, grants, etc.