Core Skills for Characters., What skills should characters have. Options

[Synner667]

One thing that amuses me is characters completely unfit for their role...
...Doctors with minimal medical skills, but high combat skills.
...Petrolhead characters who know very little about fixing cars.
...Priests without any theology.
...Special Forces characters who know how to shoot and not much else.

And so forth.

So...
...What core skills should characters have for their role [maybe 1/2 the skills they have] ??

For example, I would expect a viable policeman to have :-

Psychology
Streetwise
Police Procedures
Firearms
Hand-To-Hand combat [truncheon]
First Aid
Perception
Drive Car

I'd find a list of character roles and core skills damn useful for when I'm putting characters together - so maybe other people would, too.