I think what my concept of zombie survival boils down to is simply self-preservation. Can I do this alone? No. Do I need a huge crew of people to cover the entire spectrum in some under-the-radar microcosm? No.
I wouldn't really worry much about recruiting. As soon as I caught wind of impending doom, I'd gather up everyone I personally know:family, friends etc... and meet at the safest point I can think of. After that: no one else. Even if a family member shows up an hour late I'm not taking that chance. Further, I would dispatch the latecomer. Cold? Yes. Logical? Yes. I'll get to this point in a moment.
As far as recruiting doctors: no reason to. Once something happens (broken leg, severe flu, pregnancy) that is detrimental to the survival of the group, I would dispatch the malady.
I have a very simple equation I would follow with regards to who is allowed to stay in the group after the initial outbreak: value to the group must be equal to or greater than the amount of goods consumed.
As to why I would dispatch someone instead of simply turning them away: kill them as human and not be forced to deal with them later as part of the zombie legion. The weaklings you turn away for the sake of morals, or integrity, or soft heartedness are the same people that will be shuffling to your location dying to dine on your face.
If this seems a little harsh, just let me leave you with this: if my leg broke, or if I was late, or if I consumed more than I provided I would absolutely have no hard feelings at being killed for the interest of the group.
Although I understand the logic behind your thinking, it just isn't practical, or sane for that matter.
A) If people see you shoot someone for coming down with the common cold, since you believe they wont be able to run because their nose is stuffy, then I don't think a mutiny would be too far in your future.
B) You're going to have the dead walking around, and other dead just dead. Sickness will be everywhere my friend. If you shoot someone for becoming ill, you'll most likely have no one else by the end of the month because with all the stuff in the air from the decaying bodies, I'm sure everyone will get something.
C) I think it'd be a bit harder to actually kill your immediate family members then you may believe. Especially for something like the flu. If they were zombies, thats one thing, but for an illness that will go away within a short time frame its just....stupid.
When the time comes to it, I'm sure you'll have your mind set on what you believe, but what about the people around you? As I said earlier, if you kill someone for something so small, then you won't be in charge long.