Thinking in Circles about things I don’t understand (economics)

Yesterday, I wondered aloud on Twitter:

Wondering: why isn’t minimum wage tied to inflation so it predictably auto-adjusts yr-to-yr? How would that affect the economy?

I had a great follow-up conversation with @Brishen, who is of course, brilliant on all these sorts of things. I’m pasting below the fairly-disjointed circular logic thinking that had lead to this (this is a slightly edited version of what I asked him), and stemmed from that thought, in case anyone has any insight, or better yet, suggested reading for me (besides an Econ 101 textbook):

Min. Wage should auto adjust up over time based on “costs of living”, which I short-handed to inflation. But then I thought maybe there should be localized cost-of-living variance (which, there sort of is, diff. min wages across provinces). B/C rising costs aren’t as dangerous to small business as unpredicted changes. But that might cause flight out of urban areas to suburbs for small business? Or maybe there’ll be a slight hiccup and verything will keep on rolling – b/c it just becomes costs of doing business, which somehow, no matter how high, seem to just become part of the fabric.

if I know Min wage will adjust by 1.5% every year, then that just becomes math

And increased min wage should increase buying power at the lower end of the income spectrum which seems good.

But then I thought. Increased min wage = higher costs for business = higher prices of goods for customers = higher cost of living = higher min wage and then into an ever-increasing death-spiral of inflation.

So maybe we should abolish the min. wage altogether, but I don’t believe that’s actually a viable option. Human self-interest prevents the “market” from establishing a “fair” working wage I think.
And is a flat tax system fairer than a “progressive” tax system like we have?

For some reason, I’ve been spending a lot of time thinking about these large issues that I have no education to help me understand, and I distrust the sources I have readily available to me.