Best route for highest earning potential?

I looked up median salaries on Google for positions in the USA.

Medicine $313,000
Pilot, Lawyer $135,000
Petroleum Engineer $122,000
Business Operations Manager $120,000
Software Developer / Systems Architect $110,000

The top pay for Lawyers, Engineers, and Pilots doing international work was very high.
Doctors are only rich in the U.S. In Canada the poor guys only make $206,000. Check numbers for your country.

Building a business is where most people make real wealth.

You don't need any college to do it as there is actually a negative education coefficient to business success.

The people with the most education are the least likely to succeed in building a business. Yes there are exceptions. But, education - including business school - is all about teaching you how to be an EMPLOYEE, and jobs are not set up for your success - they are set up for the companies success. Business managers may make good money; but nothing like the owners do. It takes a different kind of education to be a business owner (and I've never met a business school professor who ever started a successful business, and most have never even tried: They have no clue what it takes).

Tell him to start a business if he really wants the highest chance and real money, wealth, and impact.

Tell him to invest 3-5 years into that with the same amount of effort (or more effort) than going to college.

Becoming an entrepreneur means becoming a student of business and of self improvement.

There are organizations out there which will assist and guide.

I suggest both of you read: "The Compound Effect" by Darren Hardy. That is a book about the basics of how to become successful at anything.

Then I suggest you read: "The Business of the 21'st Century" to give you an idea of the pro's and con's of the different business structures.

If you like that and want more information I suggest: "Go Pro" by Eric Whorre.

There is no reason why your brother (or a son or daughter) cannot actually be, or be solidly on their way, to $millionaire status by the time the people who would be their classmates are graduating from College with $80,000+ in debt.

Of course; being an entrepreneur is not for everyone.

I wish you and him well on their future,

A winning lottery ticket...

All of those are great

If you are USA, go Law, after law school, spend a couple of years at most in the field.

Then transition to politics, even while you are in school, work for political judges or campaigns.

Run for office, if you can find or get a state or higher position, even if you only spend 1 or 2 terms.
You'll get rich not necessarily from the salary but connections made.

Law

DO NOT GO FOR MEDICINE. Buissness is where it's at, but if you're not doing that then make sure you do not go for medicine. To get paid serious bank in medicine you have to put in sooo much work and get such good grades. If you're purely interested in money then putting in that much effort to get it is fiscally unsound.

Medicine, baby.

i believe of your list the lowest cost & shortest schoolin compared against best jobs prospect & pay are petroleum engineerin

fame though? not unless he blows a refinery up

Surgeon

Business has the most earning potential, of course. But fame? Become an astronaut and go to Mars, or be an international news anchor.