First and most important depends on the tech - namely, whether the uterus can be replicated or not.
If so, I’d choose individuals based on their skillsets and ability to form a colony (including childrearing professionals). I would also take along a lot of sperm and ova samples from widely-diverse genetic populations of all races so that children could be created with a necessary genetic pool.
If not, sad to say, I would have to include “healthy female with working womb” among the desired skillsets, though I would still take along lots of genetic material, again both sperm and ova, to be implanted in said wombs; I’d try to go for a 1:4 ratio of men to women. Natural reproduction would not be favored at the first stage unless the colony was huge (in the 10,000 genetically diverse individuals range).
(Note that IVF and stored gametes make colonies much, much easier; it’s simply a lot easier to haul around frozen sperm and eggs than to select the colony itself for genetic diversity.)
With all of this in mind, I would probably select partly by “crew” skills and partly by lottery. Regarding the crew, the important factor is skillset and all others are irrelevant (also, crew members with families can bring their family); for the lottery, I would probably triage individuals over a certain age or who were too disabled to work. Also, if we don’t have free access to exowombs, I’d reserve 3/5ths of the lottery to be only available to healthy women under 40 with functional uteri, as above, and these women would have to contract to be willing to bear children. (Whether they would be required to raise them, I’m not sure, though they should be permitted to. How many slots do we have for dedicated childrearers?) If we didn’t have to do that, I would probably divide the lottery between open slots and family slots.
Regarding selling slots, I assume I have control of the national government under emergency powers. Therefore, no, I wouldn’t “sell” slots, I’d nationalize the resources necessary for the project. The wealthy who might otherwise buy places on the ship will be contributing with or without their consent, so I see no reason to give them places on the ship! (That said, I imagine the Beltway politicians would realistically ensure that they had “crew” status, along with their Wall Street buddies; this is America…)