There are a few threads on taxation. I found this one, but I’m sure there are more.
Most of the discussion is about the voluntary aspect.
There’s probably not much about how much an ideal government would cost. So, I guess I’ll not merge the two threads.
So, specifically on the topic of what such a government would cost, compared to today:
The majority (about 60%) of Federal government expenditure is on “entitlements” plus welfare. That would clearly not be a part of a proper government. So, we’ve taken over 50% off.
Then, if one goes to the state and local level, the biggest chunk is education. This too will clearly be private under a proper form of government.
So, just with those two categories, you would reduce tax by more than 50%.
But, today this is pie-in-the-sky. Is there any chance at all that this will happen in your lifetime?
As for the military, I don’t see why the U.S. needs to spend as much as it does. And, much more importantly, a government with a proper approach to foreign policy would have to spend much, much less.
Added: Some other threads on the topic: here, here and here. (That’s a few hundred posts on the topic. So, most of your questions probably have responses in those threads.)