Basically it's your decision.

But a common way to start is to build up the vip/exec-seats in the arena until it is maxed out. (13500 seats) No extra coaches hired.

After that you get enough income in home games to buy and support the FULL build fittness center and the 20 fittness coaches.
(first get the coaches and after that the center, because of the 10 month wage rule)

Why full? To get the maximum effect. If you get less coaches (like 10), you have to pay the bonus again when getting the next 10.

EDIT: Common is also to start with the physical skills, because this will not increase the wage when the new season start. Wages are calculated at the start of new season, depending on the highest NON-physical skill.

yup as jack says, do it in big lumps rather a bit at a time due to the bonus required each time.

fitness is generally deemed the best first step.

i beleive in hiring the rest in steps however which is a bit different to most...

after fitness coaches i'd go for getting 20 Def coaches.
you can then train blocking tackling and agility for your players which strikes me as the best 'value' coaches.