The premise is that you’ve got five days to gather enough people to sustain human life on a new planet, because this one is about to destroy itself. The method of transportation to the new planet is teleportation, but the most that can be teleported is 20,000. There is not enough time to interview thousands of people, and you probably don’t want to tell people what you are doing, unless you are into mass panic. I used this method in a previous thread. .
How would you do it?
I’ll open with the obvious strategy:
Completely randomly.
Who knows what genes will be needed in the future? Better to take a random sample rather than overengineering yourself into a corner.
This assumes I have a mechanism for selecting 20k people at random from the worlds population. Without that I’d try to emulate it (probably badly).
Don’t let Phil Collins sing, and give Steve Hackett his two tracks per album.
One way is to see how well natural selection works. Announce the location of the teleportation portals and when they will be activated, and see who survives to make the trip. It’ll get ugly, and there may not be too many poets in the new world, but who knows? Maybe they’re more resourceful than I think. 
Go to a medium sized town (pop - about 20,000) with a decent hospital and some heavy indutry with the teleporter. At midnight, the day the world ends, I’d port the whole town over. Then I’d break the news to them. There should be doctors and some machine shops to help kick start the rebuilding of civilization. Plus, there ought to be a few farmers living on the outskirts of town as well.
I notice there are currently 78,149 members of the SDMB, so that’s out. Perhaps people with a post count of at least, say, [del]1016[/del] 1017?
Ten thousand?
How many rational people are there in the world?
In which country? Where the town originates from might determine the religion of your new civilization.
I’d hit the phone book and arrange meetings with various people like architects, scientists, welders, farmers, etc. and then poof them away as they appeared for the meeting. Overall, the idea would be to get as good a sampling of people with varied theoretical knowledge and those with practical knowledge as there is within the local area, and then look up a college with a high ratio of women that’s around ~20,000 people and just start teleporting them all away. So there I’d have a solid group of young and healthy and decently intelligent workers to hand over to the experts and get society building again.
The first thing I’d do is restrict my choices based on some common language. No taking people at random from all over the globe. After the snatch things are going to be pretty confusing any ways. If I were to add the Tower of Babel on top of that, I’d be afraid just where things might go.
If I can do what Wargamer suggests, and simply take a small city, that would probably be simplest. Hmm… with schools out for the summer, Ithaca, NY might be an interesting choice - world-class libraries, an interesting mix of technologies, and still skewed young. Blast, Wikipedia puts the population at 29,000. Too large. Okay, second choice: Cortland, NY. I know that they have a hospital, and will have a respectable library at SUNY Cortland. Even better: Wiki lists the population at 18,740, which is probably about as good as things will get for being able to match the OP’s 20,000 person limit. I grant I’m making assumptions about language fluency based on geography - but I think that’s the only method I believe the OP has left open, since interviews are not possible.
As for why did I choose Cortland, rather than, say, looking for another ethnic and cultural setting: For good or ill, that’s the setting I’m familiar with. Also, having done work for the City before, I have a pretty positive view of the people there. And I know they’ve got a decent small hospital. I just wouldn’t have any of that kind of information about a town chosen outside my area, let alone one chosen outside of my country and culture.
Seconded! 
Am I taking people, people plus what they’re wearing, people plus what they can carry, people plus tech and real estate, all of Cortland, or what.
Seriously. I’m not taking a radiologist if I can’t take a bunch of equipment, power generating materiel, and at least one or two technologists. A surgeon might be useful, if it were Jack, from Lost, who’s a medical McGyver, but without an OR, I’d probably be better off with ER docs only.
I may take a couple of engineers, but I’d probably stack the deck with farmers, bowhunters and blacksmiths, or even Renfair geeks who make their own gear.
The other issue would be not losing knowledge that we have, which we may make useful in the future. It might take me 20 years to get hydroelectric power, and I’d need to make sure that all that electricity and electronics knowledge didn’t get lose, and have to be rediscovered as in Canticle for Leibowitz.
People and what they are currently carrying with them, only.
Spoilsport! 
More seriously, Attack from the 3rd Dimension has a good point: without the technology required for many of the modern specializations, those people’s skills are going to be of limited utility. ISTR hearing that past about 1850 technological levels there’s too much “build the tools to build the tools to build the stuff” going on for a single person, or even a small community, to be able to sustain their technology without the advanced tools. Or at least a lot of time. With that in mind, I’d probably change my focus to a location where I’d know I could grab a good solid core of people with skills from that era, and people who have shown an interest in such living.
So the staff and visitors at Old Sturbridge Village are going to be in for a bit of a shock. The bad news is twofold: First off, one will be guaranteed to pick up some non-fluent English speakers (I’ve never gone to OSV without running into tour groups of people who either cannot or will not speak English.); Secondly, I doubt that would get more than 5000 people if one did a single ‘snatch.’ And once you’ve snatched people from OSV, there’s not much chance that you’ll be able to snatch anyone but LEO afterwards.
To make up the rest of the 20000 people, I’d probably go through a list of other US “living history” sites, Plymouth, Jamestown, and others. Though skewing towards pre-1850, wherever possible.
What about SCA events?
I wouldn’t rule them out, for picking up the remainders, but generally, the technologies that they’re using there are several hundred years more primitive than those at OSV. And from my experience the skill sets practiced tend to be more limited. I don’t recall seeing anyone who knows how to build or operate a saw or grist mill at an SCA event. I know there are those at OSV. I don’t recall seeing anyone at an SCA event who knows how to use period tools to bring in a crop, and thresh it. I know there are people with those skills at OSV.
I would teleport all the most primitive tribes I could find in places like New Guinea, South America, Africa, Melanesia, and… well, I suppose I’d have to do more research to find other areas. My theory is that the people who can survive with the least here, can survive somewhere else best.
BTW, I wouldn’t go with them. Ick, that lifestyle isn’t for me.
Question: Why can’t the reason for the genesis/exodis be stopped before the two days are up?
Phil
For the same reason you can’t use dice while playing Texas Hold’em-thems the rules of this game.
I am surprised that almost everyone is concerned about getting as much technical know-how through that gate as soon as possible. Is no one screening for religious, political or societal reasons? If everyone needs to speak the same language, why does it have to be English?