I say minimum wage should be set at the first level subdivision, but as an annually readjusted calculation, where one month's wages is no less than is necessary for the state/province/territory/etc.'s average rent to be at most 40% of that minimum wage.
The reason I say 1st level subdivision instead of nationally is because setting it nationally squeezes rural wage givers unnecessarily while making wage earners in urban centers starve.
By operating at a more localized level, you're less likely to run into this issue, and also it creates a gradient of wage markets which will naturally incentivize the creation of single income rent supporting jobs in economically underdeveloped regions, meaning that you can actually use the difference between the highest and lowest minimum wage in a country as a metric on income equality and equality of development opportunities.