But are you sure Carlos isn’t Nava’s imaginary friend? 
On the female side of the group, I’d think Honor Harrington would have to have a spot. Accomplished leader, teacher, warrior and problem solver. And as a bonus, she has excellent genetics, including a bit of a heavy-G adaptation.
Some great suggestions. I’d add, for your consideration:
Dr. John H. Watson - We’ll need a doctor, and he’s a stalwart, hard-working one (much as I hate to admit it, Holmes probably wouldn’t be cut out for a situation like this). I presume for purposes of the OP that he’d know 21st-century medicine… although, given the hypothetical, maybe he wouldn’t need to.
James T. Kirk - Resourceful, lucky and definitely has an eye for the ladies. Just watch his kids dominate the gene pool after the first generation.
Montgomery Scott - Can figure out and build anything.
Robinson Crusoe - An expert on making do, and thriving, with limited resources.
Mixtli - Hero of Gary Jennings’s novel Aztec. Brilliant, resourceful, lots of wilderness-survival experience, and a very strong libido.
William Mandella - Hero of Joe Haldeman’s military scifi novel The Forever War. A survivor, very smart, very lucky.
Marygay Mandella - His wife. Ditto on all counts.
Friday - Heinlein’s heroine, from the novel of the same name. Uber-competent and smart.
Eowyn - Someone suggested Arwen earlier, but she’s an Elf, and not eligible according to the OP. Eowyn can take care of herself, is used to living under primitive conditions, and has strong leadership skills.
That juvenile delinquent girl that Bart fell in love with - Anyone who can escape from Juvie Hall during a dance after breaking Bart Simpson’s heart is gonna do just fine after civilization as we know comes to an end.
Sydney Bristow - I don’t watch Alias much, but she seems to be able to get through just about any crisis in style.
Ellen Ripley - Someone had recommended her earlier; I strongly agree.
Samantha Carter. Smart, beautiful, intelligent (I think she has a MD among her other qualifications)
Jack O’neil. Courageous, brave, would fit the fighter image.
Zena. Another warrior very breedable and resourceful.
Another vote for Laura Croft. We need Laura. Period.
From the OP:
Human is preferable, but not necessary. Arwen is of Earthly stock and can breed with humans, so she counts. Perhaps a somewhat odd criterion, but that’s what the OP chose.
I considered Honor Harrington, but we can’t have her without Nimitz, and I don’t think he’s allowed. For the benefit of those not familiar with Honor Harrington, Nimitz is a treecat, an alien arborial creature with an empathic bond with Honor (often mistaken for a “pet”, but that’s an insult to treecats). 'Cats are about as smart as humans, though less technological, and until recently they’ve hidden their intelligence from most humans. They have very quick reflexes and formidable natural weaponry; in close quarters, it’s plausible for a single treecat to take out 3-5 armed humans.
For that matter, I’m not convinced that it’s a good idea to have people like Honor, genetically-engineered to be extra strong, tough, etc., even if they’re allowed. Such strength generally comes at the cost of a greatly increased metabolism, so the character has to eat vast quantities of food. This isn’t much of a drawback in a functional modern (or later) civilization, where the usual problem is too much food, but in a post-apocalyptic subsistence situation, Honor would probably starve.
Elendil’s Heir–
Watson’s no good, as both Buckaroo Banzai & Doc Savage are physicians & surgeons, with additional skills, & physically superior to boot.
Friday is more than human, & barred by the terms of the OP.
Both Kirk and Scotty are well worth considering.
No one’s mentioned River Tam from Firefly. She’s a warrior, incredibly smart, and has all her good breeding years left. She’s fully human, since the Firefly 'verse doen’t have aliens.
StG
Actually, if you had to pick a single prepackaged group as a whole, the crew of Serenity would be a pretty good choice… a wide variety of skills, 4 women of breeding age, and it would clearly result in the wittiest society ever.
How so? Just because she was a genetic construct? So is Athena, but she’s still human. Friday would have to get her fertility restored, but Buckaroo or Doc or Ishtar could handle that easily, especially if Teena was advising.
Her physical performance exceeds Human norms, & she may even be a genetic chimera, as far as we know.
I propose that DNA juggling, via Genetic Engineering, is right out.
Why would you bother with a copy–Oliver Queen–when you can have the original, Robin of Locksley?
Robin would be a better choice all around. Green Arrow always seems like a prick with a bad attitude. Robin Hood was able to get along with people and created a whole new merry society from scratch in the woods, GA can only get along with buxom women in fishnet stockings.
OP chiming in—genetic engineering and chimerism are acceptable, as long as A) There is no extraterrestrial genetic information included, and B) the genetic tampering does not confer powers or abilities beyond all possible human ability. (So, having the mental prowess of an autistic savant without being autistic would be OK; being able to tear apart tank armor with one’s bare hands would not.)
Didn’t friday have Terrestrial non-Human DNA added, too?
Animal DNA?
From Hartley M Baldwin’s (Boss) posthumous letter to Friday: “…but you can take pride in the fact that all of you was most carefully selected to maximise the best traits of H. sapiens.”
On that basis, I think Friday would be excluded. I don’t know if it’s ever stated explicitly, but it’s strongly implied that her reflexes and senses are beyond the capabilities of any non-construct person. On the other hand, Minerva and Teena, though fine specimens both mentally and physically, are not outside the range of human possibility in any regard, so they would still be allowed. On the gripping hand, though, we have several candidates with multi-century lifespans, which is certainly beyond the range of human ability, but nobody seems to object to them.
You got to wonder a bit too, the primary contributers to her genes were both minor telepaths. I think I recall it being mentioned that Joe and Gail were the largest sources of her DNA.
Jim
“It is not possible to define your relationship to them but it is the equivalent to something between granddaughter and great-granddaughter, the rest of you being from many sources…”
Wow, fast with the exact line, I can only do that with Tolkien. So she has a good chance of being a latent telepath. Does that exclude her from the Op’s criteria?
Jim
Only if you want to start another **paranormal abilities ** brouhaha. 
Besides, the book was still right beside the computer from the previous post.
My first couple thoughts were more classical.
Odyesseus. Smart, strong, resourceful, patient, great leader.(And I’m pretty sure Human concieved)
Daedelus: Genius, Inventor, tool maker, very handy guy.
The rest I was thinking of seem to be god decended the more I look.
Again, there’s some ambiguity here, based on the OP saying that Arwen would be allowed: Her great-great-great-grandmother was what amounts to a minor goddess. I think that lest we start down too slippery a slope, we ought to just ammend the OP to disallow Arwen.