Most of the following staff is unemployed at gamestart, so that it also should be possible to sign them if you're managing a smaller team.

Good Coaches / Assistant Managers
Look for staff with high attributes for: Coaching Outfield Players/Goalkeepers, Working With Youngsters, Motivation and Tactical Knowledge. Judging and Man Management attributes should also be good. Your Assistant Manager controls your reserve squad if you don't.

Good Scouts
Scouts are very important, especially for small and medium clubs. When you go to "player search" you can only see very famous and regional players - when you sent your scouts, they'll also find that great australian striker you couldn't find. The most important attributes for scouts are Judging Player Ability and Judging Player Potential.

Good Physios
A physio treats your (injured) players. The better he is, the faster your players will recover. Very important for physios is the -big surprise- Physiotherapy attribute. High ratings in Man Management, Motivation and Discipline also wouldn't be bad.

Player/Coaches
Every player older than 30 can be assigned as a player/coach or player/assistant manager. But if you ask me - I mostly prefer "normal" non-playing coaches. Though, sometimes this is the only way to get decent coaches to lower division clubs.