There is a standard, generic incoming doom.
The general population is already roughly aware how nasty the situation is. (with both people overreacting and underestimating the problem)
There is an Organization that can save approximately 1 million people (with soft SF means, sorry about that ;) ). It is effectively flooded with prospective applicants who want to be taken.
A few people (like some politician kids) has to be taken just as a racket paid to politicians of great powers to make them cooperative, however their share in the gene pool is relatively minor (less than 1%);
There is clearly a need for experts necessary for survival, (round 10%) but even among them one can be a bit picky;
For the rest of people there are at least 50 candidates per place; (one don't ask for any special skills in particular, they would have to be flexible anyway)
The Organization don't want to choose the rest of lucky ones at random, but want to apply some rational mechanism of selection - they want people who are young, healthy, fit, hard working, able to populate new planet, intelligent, educated and not making troubles; (unofficially also: easy to govern)
The Organization, if given a chance, would like to weed out genetic problems or transmittable diseases; (nothing personal, but if they have two similar people, and have to chose one, the one with hereditary problems is left)
The Organization is neither politically correct, nor racist - it would not disqualify anyone merely for his race, nor would it care at all for keeping any ethnic quotas, nevertheless it would be interested in maintaining genetic diversity;
The test have to be done rather quickly (a month or two, tops) and can not be prohibitively expensive;
Asking for showing any medical history or medical history of relatives is possible, however, people would be desperate so if only asked would gladly admit being offspring of people living as long as Methuselah (not mentioning that a few might even try to forge documents confirming such claims);
There is no special preference for countries as such, but as you know when there are some life boats filled it's always: women, children… and first class passengers, so selection would be presumably somewhat biased in favour of more developed countries.
The Organization is aware that the starting condition would be harsh, that people would hard to coordinate or force to do something (there is megafauna, so people would really have to be armed) and would like to avoid any split/rebellion based on ethnicity, religion, political orientation, or general dissatisfaction. The Organization would like to maintain some kind of state of emergency for a decade and later build a semi-democratic system with serious technocratic bent.
OK, which reasonable selection criteria to apply:
Which tests should be applied aimed at which genetic (or transmittable) diseases? Should genetic tests be run or maybe rather analysing phenotype would be easier?
Any tricks during selection to process to boost loyalty and social peace?
What should be long term outcome in next generations? (Which diseases would be eliminated / reduced? Would there be any side effects? Any social impact?)
So my types:
Test for IQ or some more extended test, to get roughly fair comparison (instead of deciding what counts as good school)
Age preference (for men around end of university, for women, because best biological time for pregnancy is around 20, then actually a bit younger)
Screening for all serious disabilities mental disorders (like schizophrenia) or disability, any mild problems would be ignored, as the detection rate may vary
Screen family history, extra points if can prove that relatives live long in good health
Screen for monogenetic disorders
Screen for AIDS, STDs, tuberculosis, etc.
Provide general health check and fitness check
As single men tend to be more active in any revolution, better provide a sex ration with mild overrepresentation of girls.
Mix the groups so each would have properly diversified background, thus make any ethnic based faction harder
Ask people to do some rituals boosting their loyalty, like signing the constitution, make official plea, whatever. To make any rebellion harder:
play according to the declared rules
make the rules somewhat one sided, but technically speaking leave a big place for working within the system, and just show any troublemakers, that regrettably they failed to find proper supermajority thus their idea is shelved
allow local level democracy - people would be hard to supervise anyway and in some cases the central gov would not be blamed for some local failures
Based on studies concerning adopted kids there is a strong relation between IQ and genes, so as long as there would be no total collapse of educational system, such society would in long run have rather high IQ (or other mental metrics)
Monogenic diseases would be seriously curbed (but in practice the result on public health would be mild)
The population would be too small for some infectious diseases (like flu) or it would eradicate the overlooked cases of ex. HIV. Possibly there would be even some level of overreaction.
There would be a baby boom and its echoes in next generations. The result would be even more severe than baby boom after WW2. It would put an extra strain on children/elder care.
There would be one generation in which may have troubles with equal rights, as selection of younger women would cause lower educational level. That would be almost leveled in next generation, at worst in two.
Big part of new generation would have mixed racial background, racial discrimination may be perceived in the same category as witch burning.
If any positive and clearly visible outcomes of such selection happen, then eugenics may be perceived more positively, what would affect law system.
If the emergency powers are not abused seriously, then some of them may be more accepted by the society. (Americans: think how in other countries guns were confiscated or national ID card issued) Needless to say, if there is a serious abuse then whole project may end in a one big civil war.
I’m especially interested in long term consequences and possible backslashes, side effects, etc. The whole selection process would just serve for back story, where quite rational selection process would simply shape the society with its own special characteristics.