We don't really know anything about this yet. Other than you can save your points.
The way I read it was that you had one of each type of GP to choose from, however each one represented a particular RL individual who had varying abilities.
Could be once you choose one the whole list changes, not just the Scientist, or whomever it was that you chose.
Also you have to remember that each game will have different circumstances leading up to you GP choices. In one game you may need a General in the next you may need a Scientists or Prophet. So the order in which they are listed seems very unimportant and would be very difficult to game.
It's worth to bring the Founding Father system, nevertheless, as is something that could be relatively similar (not exact, I think, because they imply you don't know which your next GP is until the available one is "hired"), and it is something that has ben done already in the series (or in a close familiar)
Basically, you have an ordered list of GP, each providing a benefit, and each with an increased cost in GPP (In Colonization, Political points, with added specific points on each of the FF branches: military/exploration/economic... > In CivVI I guess each branch will use its own type of GPP)
You may chose the first Great Person is offered to you (as soon as you reach the needed point treshold), or save for the next, more costly, one. Once you pick one, your GP counter goes back to zero (or maybe saved points minus GP cost), so you are at a disavantadge for the next choice with the civs that have still not got a GP. As the costs increase, it is not easy you are able to get two GP in a row, but if you GP production is high enough, you will surely be able to advance other civs before they are able to choose a GP.
Main difference seems to be you are not able to see the full list, and opportunities for the next GP are only made available when the current one is choosen by any civ (in Colonization, you are able to "save" for the one you want, but you will miss already all Founding Fathers you rejected in your beeline to the desired FF)
Nevertheless, it is a nice cost-oportunity mechanic: ¿do I get the GP now and start benefiting from it, even if it is not the ideal bonus? ¿or do I wait X turns for the next one, checking if its bonus is better?. Depending on bonuses balance re-roll should not be an issue, except may be for "perfect"-targeted games.