If there were 10 people that were going to start over, wouldn't there be severe inbreding after the first few generations? If the human race ended up like Appilacian Hicks, I'd rather they'd die out and the lizard mutants take over.

But anyway, here's who I'd pick:
Historian, someone's gotta have a record of the past to know where we came from.
Scientist, depending on the field, can keep the sciences and development going and possibly medical stuff if they are trained as such.
Naval Officer, key leadership role, plus has nautical and military skills. Also can tie knots.
Shop Teacher, builder and craftsman, also capable of doing maintainace of the bomb shelter.
Preacher, this is more of a moral choice, faith can get people through tough times and can also be a councelor/confidant for people in the new era.

High School Cheerleader, what can I say, I have a lolita complex.
Artist, the world needs creativity and badass tribal designs.
Chef, food preperation and sanitation, food = morale.
Housewife with child, 2 lives in one, plus the child will easily adapt and be socialized in the new world. Housewife would be capable of acting as a midwife for future children later down the road.
Teacher, only if she's a hottie or a milf, someone has to be able to teach the younger generations.

There we go, my list of people to restart the world.
"Remember how much fun you had shooting spitwads at the teacher in seventh grade? Imagine applying that kind of attitude to actually fucking with Mitsubishi!"
- Jello Biafra