The "ideal minimum wage" would be the total cost of food, healthcare, transport and housing as recommended by the experts in each field for providing a quality and quantity of life such that for the simple majority of people on those wages, it would require a disproportionately large increase in wage to significantly impact that quality or quantity of life.
In other words, they are not suffering actual, measurable harm by being on the minimum wage versus the alternatives (leeching off others, going onto welfare, becoming a survivalist, becoming a member of the criminal class, etc).
(No, not all criminals are "just trying to survive", but anyone who is just trying to survive is going to consider crime a valid alternative to eating roots and berries.)
The "practical minimum wage" is the best available compromise between what wage-slave masters will tolerate and the ideal minimum wage. Wage-slave masters don't give an f about your health, even though it costs more to replace someone than to keep them healthy and functional. They don't give an f about anything beyond their day-to-day profits, the actual economics be damned. Odds are, many are guilty of criminal activity already, so to them one more crime means bugger all.
If you have no minimum wage, these people would pay as close to absolutely nothing at all that they possibly could. Some already pay nothing and use fear and intimidation to insure there's no trouble. If you raise minimum wage by anything at all, a few more bosses get added to the number. You can't escape it. But if you increase it by just the right amount, the number of people who gain truly functional lives outnumber the ones who become trampled on further.
Of course, if the US did something rational, like adopt universal "free" healthcare (ie: distribute the cost across everyone), legislate that nobody could be involuntarily homeless, and adopt other rules considered basic human standards by the rest of humanity, then you could actually LOWER minimum wage since there would be fewer expenses that minimum wage would need to cover.