For new teams I think most people would recommend a doctor, trainer (if you have trainees) and a youth trainer (if you have 18-19 year old trainees).
Prices vary depending on various factors, but here is a rough suggestion as to prices you might pay:
* An advanced (level 4) doctor. Signing fee close to $0, weekly salary around $12k or lower.
* An advanced (level 4) trainer. Signing fee up to $50k (if you search well you may find cheaper), weekly salary around $15k or lower.
* An advanced (level 4) youth trainer. Signing fee close to $0, weekly salary around $12k or lower.
Some also recommend a basic (level 2) PR manager with a speciality, as the speciality gives your home or away performance a very small boost. You can get one for close to $0 signing fee and $5k weekly wage.
A Sports Psychologist may be useful for teams at the higher levels, but is unnecessary for a new team in it's first few seasons.
A Nutritionist is rarely used unless there is a specific need, it's possible you may never hire one.