There are many people who are out there that would be useful for you in the event of the zombie apocalypse. Just because someone isn't on this list doesn't mean you shouldn't let them in your group. In the apocalypse you just don't know who may one day save your life.

A chef

Not because they can just cook, they have a range of other skills. Chefs are handy with knives and are great at working under pressure which they get from working in a kitchen. Some chefs also know how to forage which means more food for you and your group.

A leader

For a group to function, you may need a leader or a council or something like that. It's easier to make decisions this way. A good chain of command would make things easier for everyone because this means it isn't anarchy because everyone wants to do different things.

A communications specialist

At some point you may need to talk to other people. Whether it's another group that you want to keep in touch with or in case you have a chance to communicate with other countries to find out whether the know anymore than your group does.

Anyone with medical expertise

This one is obvious, you're in a zombie apocalypse. If someone gets hurt you couldn't just take them to the hospital.

Scavengers and scouts

Both are quick, quiet and are observant which are useful in the zombie apocalypse. They would kind of be like what Glenn was for Rick in the beginning of The Walking Dead where he helps him escape the zombies. If you send out groups, keep them small because you don't want them drawing too much attention.

Engineers and Mechanics

Kind of obvious, you will need cars to escape some situations and you'd be in hot water if it broke down with a hoard of zombies around you. Plus they can deck out the car and try to zombie proof it.

Survivalist

Also obvious, what better way to survive than with someone who has been training to survive, they know a lot.

Agricultural Expert

When you do find a place to settle down, I doubt shops would be up and running. You're going to need someone who could help you grow food and things like that.

Fisherman

Fish are going to be one of the most plentiful foods you can get as I doubt zombies can swim as they move too slow. If you have an expert fisherman/woman you'll have more food and they can teach you.

Lookout or Marksman

You'll need people who can shoot really well and people who can watch your back while you and your group are on the road.

Guard or Soldier

Again, these people will know how to shoot and kill the undead as well as surviving everything. Soldiers are used to working in groups and know where military bases are which may be useful.

Hunter

This person can be able to catch food and have essential skills which you will need to survive. They can use a weapon, have experience and can track as well as a load of other things.