Before I get to my choices. I'm of the opinion that there are three things required of a survivor in any apocalyptic scenario, and since I am a fan of setting things up before revealing other things:
The first is a fast paced intelligence. It's not enough to be smart, you have to be smart at a moment's notice. You have to make the smart decisions without having to think about it. The best way to express this is by having various talents. Both physically and mentally.
The second thing you need is patience. It's not enough to wait days observing an area. It's not the patience to stay put while someone heals or until the food runs out. It's not the patience to wait for your traps to spring. It's the patience to wait for the right moment. The ability to recognize the right moment is related to the first thing you need, but waiting for it is just as important. The right moment could be the right time to strike, to eat, to sleep. In the apocalypse, any apocalypse, you can't do things when you want. There are different factors to think about. The right moment could be right now, or days from now. You have to be patient and not get overzealous just because of emotional components.
Speaking of emotions the third thing you need is control over them. Getting angry and making a bad move, getting lonely and trusting the wrong person, or being afraid and unable to move can all cost you your life. It's not about being emotionless. You can have emotions but just don't let them have any impact on thing one and thing two. The ability to clearly access a situation is probably the most important thing to have in your arsenal.
That's how you survive on your own, and while a partner should have all those things it's important that they have something else. Loyalty, a sense of justice, and a goal. So I guess you need six things. A sense of justice makes sure they won't pull any dick moves like robbing or murdering you. Loyalty makes sure they won't ditch you or betray you for a better deal. Finally a goal makes sure that your group has something to do and the hope to forge ahead. That may not seem important, but if you're surviving just to survive than it's my opinion that you're more likely to give up when under duress, at least fictionally speaking. So then what three characters fit that bill.
The first is probably the most obvious. The great Sherlock Holmes. In this case I'd require a more modern Holmes so his knowledge base would include newer technologies. So Benedict Cumberbatch's Sherlock suits the need just fine.
What Holmes offers a group:
An almost perfect reading of any future members or wanderers we would encounter. A near perfect assessment of any area we wish to move into or stay at. The ability to spot traps or deduce intent of possible enemies. Holmes offers information. Which is the key to victory. Go ahead try and think of scenario that would be easier without Sherlock Holmes.
Holmes is only loyal to people he likes so earning his loyalty is an issue. He's also suffered from a drug problem in every iteration of the character but this one is the least pronounced.
The second is probably the least obvious, Bulma from Dragonball Z (preferably Frieza arc Bulma.) A scientist is required to create new ways to achieve the impossible. Bulma is the smartest scientists that fills out the earlier perimeters. Any other scientists of her level are either evil or only concerned with their own interest.
What Bulma brings to the table:
Bulma started out in Dragon Ball as a wanderer so she's accustomed to the life style. Plus Capsule technology would be invaluable, it is truly a game changer. Bulma has reverse engineered every piece of technology she has encountered. Including an alien spacecraft, and super advanced androids. In an alternate timeline Bulma developed a time machine. So if we run into anything we don't understand Bulma will understand it. She also developed a radar that can track magical items at the age of 16, that's just plain impressive.
Bulma is not known for her patience, and she can be stubborn and arrogant.
The last member of the team would have to be the moral core (I'm sure as hell not). A good moral core is hard to find, but it'd keep us honest and I think that's important. So while there's lots of good ones to choose from no man off the top of my head (haha oh Dave) has more valor and honor than Ned Stark.
What Ned adds to the cause:
Besides the ability to basically trust him never to stab you in the back or break a promise on purpose, Ned is a proven warrior. And while a younger more physically capable Ned Stark would be preferred even the older Ned is capable of handling himself just fine. I just think he's a good fit.
The only real downside is that he might be out of his element depending on the cause of the apocalypse. If we're dealing with zombies he's fine, aliens not so much. Robots I kind of doubt it. However his main downside is that he's not the brightest bulb, strategically speaking. The rest of us would have to guide him.
And that's my list, and my reasons for it. Hope you agree or at least enjoy the read.