I say everyone who will take the oath. The book focused on titans of industry, but I imagined there were many other people there who had no ability or desire to be industry leaders. Maybe they wanted to be collect stamps and spend time with their families. The guy who recounts the story to Dagny about how the workers at the motor plant turned on one another is an example. His description of how the policy brought out the worst in everyone was one of my favorite parts of AS. The administrator whom the workers had to go to whenever their families needed something stands out in my mind as one of the worst villains. That worker, just wanting to live free and make honest trades with other humans, stands out as a hero. I imagine it needing diversity of people, some titans of industry and some completely uninterested in industry, all living for their own interests using honest mutual trades with other people.

I'd like to see the people take an entry test based on philosophical principles. Using situational questions to determine how they would react in various situations.

Before I got to be a Galt's Gulch habitué, my attitude was that of the Amish person who was asked whether he knew anyone who wasn't sinful and replied, "I'm sure that they all are except thee and me. And I'm not too sure about thee." Since then I have met and corresponded with a number of probable Atlanteans.

The first one I thought of was Bruce Schneier. A cryptography pioneer whose tech helps people communicate secretly. It would be bad for us if he went to work for any state. I'm not sure what his politics are, except that he sits on EFF's board.

Reaching into the past a little, How about N. Tesla, A. Einstein, T. Edison? In todays world, S. Hawking and R. Penrose.
I would also, like CircuitGuy include those who and taken the oath and lived by that oath. Demonstrated their ability to actually live by it, not just say it.

The real Atlantis is the USA with laissez faire capitalism where citizens are free and do not have to take a crappy oath to some disgusting government officials. Who wants to live with fear that some government official will misconstrue your actions as breaking an oath? Hiding is no way to live. Notice that the people of Atlantis did not intend to live their lives in the Gulch, rather to get out as quickly as possible and recreate a USA worth living in. Why is it even considered that one should ask certain individuals to join the country, Atlantis in this case? So you get all your buddies in so you can play poker or golf with friends. A country needs privacy for all individuals and not a lot of busy-bodies watching you as some some religious groups do or as in collectivist countries. Do you really want an even more restrictive country than what the USA is at present? It appears so.
Early in this post, I see that no one so far would want Ayn Rand in the Gulch and some would like a lot of dead people or a Platonist like Roger Penrose who actually believes that there is an actual reality where mathematics lies.

Water, Power, Construction leaders.

Suppose we start with Elon Musk of SpaceX, Tesla, and Solar City?
Jeff Bezos of Blue Origin?
Robert Bigelow of Budget Suites and Bigelow Aerospace?