Buckaroo Banzai should definitely be considered. Not superpowered, but a world-class surgeon, a virtuoso musician, and a good guide of morals and ethics.
Dr. Strangelove
- the eleven most beautiful women listed above
I may be wrong, but I believe Lazarus Long also had farming experience.
My friend Carlos, who is a very geeky agricultural engineer and, unlike most of his students, was born in a farm. Mind you, we’d need some geeky girls, but I’m sure he’d be happy to do his duty for the species if he got the chance. And I am listing a few geeky girls.
Leonardo DaVinci, who hit both sides of the street and may have been the most inventive person ever. We’d just ask him to point himself in the right direction now and then.
Rodrigo Díaz de Vivar for muscle with brains.
Marie Curie. Ok, if you don’t want Marie, then Heléne Curie.
I can’t remember any of their names, but there’s some female Ministers (as in government, not religion) in Africa who are doing helluva jobs. College degrees in several different subjects, multiple children, enough balls for a whole tribe.
At least one of the women should be a doctor, preferably with training in “traditional” methods (that is, one who wouldn’t freak out if she couldn’t get Tylenol); one should be a chemist. I’ve already listed the physicist and a couple engineers. Someone with good documentation skills would be a plus for upcoming generations.
Indiana Jones: He’s resourceful, witty, quite the ladies’ man, and if we’re talking a post-apocalyptic scenario here, someone’s going to have to go raiding old military bases etc for supplies and salvageable tech… and who better for the job than Indy?
MacGuyver: For obvious reasons already outlined in this thread.
Professor Hubert Farnsworth: Sure, he’s senile and ancient, but he’s also a Scientist, dammit! His science and medical knowledge would come in VERY handy, I’d say.
Edmund Blackadder: He’s scheming, manipulative, witty, sarcastic, and still manages to have kids to ensure the continuance of the Blackadder name. A perfect candidate.
Dave Lister: Despite being a slob, he’s done pretty well for himself as the Last Human Being alive…
Tyler Durden: Sure, he has some “Radical” and “Extremist” ideas, but you’ve got to admire a man who can make explosives from soap and harness the power of Fight Club to nearly bring down society in the first place…
Turanga Leela: She’s female, kicks ass, resourceful, and knows how to fly a Space Ship. That’s got to be worth something!
Sarah Connor: Well, she managed to fight Terminator Cyborgs, and she went on to have John Connor, which means she can take care of herself AND have kids- very useful.
Tricia McMillian: Astrophysicist, survived several years in the company of Zaphod Beeblebrox without losing her sanity. Another strong candidate.
Ellen Ripley: Again, for reasons outlined in this thread
Sylvia: (Monica Bellucci’s character from The Brotherhood Of The Wolf)- Intelligent, seductive, and hot! 
Lois Griffin: Surprisingly more versatile than she looks. Also hot (as far as cartoon characters go, that is!)
I think a 7-5 female-male ratio is good. As Chronos pointed out, ratios like 11-1 will give genetic problems. Additionally, I think many of our picks will be used to monogamy.
Female:
Jessica from Dune. (I guess the Bene Gesserit stuff is borderline superpower, but I think it’s acceptable. And of course really useful.)
Mathilda from Léon. This is in order to have someone who will be fertile in 15 years, so we don’t have to wait too long for the next generation to grow up.
Britney Spears. Because we can count on her to put out a child each year.
Male:
I second MacGyver
Will Hunting. As he is far, far more intelligent than the person who won the fields medal, he must be the most intelligent person on earth by a good margin. That should be useful.
We would need someone who is a good shooter, in order to hunt. Like Harmonica from C’era una volta il West, or something similar. If there aren’t any guns in the post-apocalyptica I’d pick Robin Hood.
Dr. Gregory House from House. To get a doctor.
Some farmer who is acquainted with old fashioned methods. The only person I can think of is Almanzo Wilder, who lost his farm.
Howard Roark. To design the buildings. And also to hold long boring speeches, so that everyone will go back to work instead of listening.
No wait, Almanzo isn’t even fictional. Im drawing a complete blank then.
The OP was looking for fictional people. There were a couple of similar threads asking about real people a few months ago in IMHO I believe.
Atticus was my first thought too! In a destroyed civilization, the qualities you mention have to be sustained.
I’d also nominate Katie Nolan from “A Tree Grows in Brooklyn.” A strong, resourceful woman.
Scarlett O’Hara, Melanie Wilkes and Rhett Butler will also work at getting things back to normal (but not Ashley). Though Melanie isn’t good for child-bearing.
A minor fictional character by Larry Niven who was sorta background to The Moat Around Murcheson’s Eye and who got a novella to herself: Brenda Curtis. A refugee from a Sauron superhuman breeding programme, she’s human but genetically engineered to be immune to diseases, fantastically strong, to have a liking and aptitude for bearing children, to be able to live off anything that has carbohydrate, fat or protein in it no matter what it tastes like, and even to be impervious to sunburn. It’s pretty much literally true that she could put in hard physical labour until the contractions were coming five minutes apart, and pick up again as soon as she’d given the infant its first suckle. And her kids would be quite kick-ass too.
Kick Holmes to the curb. While I greatly admire him, it’s a matter of recorded fact that he is woefully and wilfully ignorant on all subjects that cannot help his crime detection. A shame, as he is a prime physical specimen with a first-class brain, but that which he knows about would be little help to the repopulation programme.
Consider a place for Tarl Cabot. I’d back him to match Conan in a fair fight, and he has the advantage of a 20th century education. He is bright, has a long-term track record of getting out of trouble, and his courage is legendary. Don’t worry about his propensity for enslaving women. Since our tiny colony would presumably all share a Home Stone, his codes would prohibit it.
Minute my vote for a balanced sex ratio. If you skew it miles in favour of females, they’re all either constantly pregnant in order to justify this decision (when the one poor male bastard is working his balls off to provide for them) or else a proportion of them are just acting as men with less muscle. That and an eye on the genetic diversity; also, taking just one or two men is putting all your huevos in one basket.
Told ya!
Lazarus has experience as just about anything - farmer, doctor, explorer, tamer of planets, etc. But I agree that we need more women than men. Just not 1-11.
Snow White
Jo
Meg
Amy
Beth
Grumpy
Sneezy
Doc
Bashful
Happy
Dopey
Freddy Krueger
Ideally, we should pick characters who are both physically and mentally fit, and who provide a broad range of skills. For obvious reasons, we should avoid introducing any close biological relatives. With this in mind, I propose the following candidates:
Bruce Wayne
Terry Sloane
Angus MacGyver
Buckaroo Banzai (I would nominate Clark Savage Jr., but I want to put his sister in the mix.)
Professor Roy Hinckley. (Okay, so he’s no physical marvel, but he obviously has the relevant skills in great abundance.)
Walter Mark “Prof” Haley
Pat Savage
Barbara Gordon
Emma Peel (rowr)
Michelle Dessler
BTW, I also advocate a balanced male-female ratio. At the very least, it should help stave off romantic conflicts.
Adam and Eve. They did it once, they can do it again.
We’ll need Survival experts:
Alan Quartermain- survival, hunting, heroic.
Tiffany Aching (“Wee Free men”) scads of knowledge about herbs, sheep, and common sense.
Apparently Noah’s family would be just as good. I guess we were all trying to stay with realistic fiction, and not something this far fetched. 
Jim
But then we can’t include my choice of Thandi Palane, since she’d kill him on the spot. So would some of the others, but that’s part of Thandi’s job.
Then I’d like to nominate the obvious: James Bond. He’s as physically and mentally fit as they come, he’s as virile as anybody, the ladies like him and he has absolutely every skill that the plot requires him to have. He’s never fenced before but when the plot needs him to be able to fence, then damnit, he’s an Olympic-level fencer. When the plot needs him to fly a Russian fighter plane, he does so expertly, while fighting off a Russian soldier at the same time. He knows every single thing he needs to know, every time. That’d be a pretty useful ability.
But never, really, as far as we know, a scientist. He’s smart, yes, but not world-class. What Long is first and foremost is a survivor. He’s capable of working his way out of trouble better than anyone through his long experience. Plus, he’s got that default ‘live 250 years without medical assistance’ mutation that’s handy. (Note: that’s not enhanced…it’s a natural mutation from before the Howard Families breeding program could be expected to produce results.)
So he’s in.
Angus MacGuyer is an excellent choice as a good jackleg enginner/problem solver is useful as all hell. He’d have to get over the gun phobia though.
What about Teela Brown? She’s the result of a breeding program for luck. She does nothing active but the breaks go her way. Since it’s just a breeding program would she count? There’s no engineering involved.
If you want a man of action what about Kimball Kinnison? That Lensman was a true badass in a fight. Could be useful.
For the men I recommend:
Lord Greystoke aka Tarzan (from the books, not the movies) high IQ, strong, resourceful, really, pretty much a combination of Holmes and McGuyver with a little Conan thrown in for good measure.
I’ll second
Buckaroo Bonzai as probably the most competent character ever conceived, so, he’s got brains, artistry, and looks–plus he’s a decent fighter.
For the 10 women, we have to consider many things: Breeding ability, intelligence, and skill sets that will have to offset the deficits of the two males.
I’ll start with the Mythologized Pocohontas – attractive, intelligent, knowlegeable in the ways of the forest, and a peacemaker–a big picture kind of girl. (shoot, I just thought that may break the rules–if it does, I’ll reluctantly toss her and find an alternate).
Cleopatra Jones because she’s gorgeous and can kick ass.
Dr. Sarina Kaur East Indian, head of the Chrysalis Project which eventually lead to the Eugenics wars in Star Trek. She is a Geneticist, brilliant, and (in Trek anyway) the mother of Kahn Noonian Singh.
Rose Tyler Resourceful, can face fear, attractive, bright. (Dr. Who–currently showing on SciFi Channel)
Elena Montero (Catherine Zeta-Jones in Zorro) see Rose Tyler above – plus she’s great in a fight.
Anne Shirley Educated, smart, resourceful, and inquisitive.
Sayward Luckett Wheeler from “The Awakening Land” bright, schooled in homemaking skills (somebody’s got to bring that to the table) and believes children should have something to live up to. Stong as well.
Jesminder ‘Jess’ Kaur Bhamra from “Bend it like Beckham” not bound by tradition, athletic, bright, quck.
Mulan Stong, honorable, a good fighter, bright, optimistic.
Red Sonja again, because she can fight (everyone is going to have to do that), is strong, and resourceful.
Judy Robinson (Movie, not TV) brilliant scientist, tough, uncompromising, able to focus.
Lois Lane bright, inquisitive, forceful, capable, athletic.
Judy Robinson and Lois Lane are possible substitutes for Pocohontas, though if she stays on the list, then, they should go. This list doesn’t represent as much cultural diversity as I would like, but, unfortunately, it does represent my own literary bias and history. There is a lack of females from older literature because many of them were portrayed as lacking the primary requisites I felt necessary for repopulation. (strength, fighting ability, and a get things done attitude).