The impact of a PR is not clear to anyone. Some people suggest a higher level PR might not bring in enough extra revenues to justify his higher salary. It has never been definitively proved either way. My personal opinion is that the PR has an effect, probably enough to justify higher salary but for 99% of the teams it is not significant. Presumably if you have NT players who bring in higher merchandising, the PR manager will boost that too, so there the benefit should be clearer.
The doctor on the other hand is key for 2 things:
1) Reducing injuries obviously. This is also anecdotal evidence, but higher doctors usually lead to fewer permanent injuries and shorter injuries as well. It's likely that the doctor level determines the length of the injury, so if they shorten it enough it goes below the level where it becomes permanent and the player is ready to play again after the game. The effect is there, I think Advanced or Competent (if you feel lucky) is the most cost effective and in particular if you have top tier trainees, you will not want to be cheap on the doctor.
2) Massage specialty. This affects the GS especially for players who play more than the optimal minutes. Personally I think the most important specialty among all staff, followed by Fitness, Career Extension and the 2 small bonuses the PR can grant.
So if I were you, considering you have the issue of the arena and small profits, I'd go with competent with massage specialty. You might probably get one for less than 10k salary per week without spending a fortune. In general terms I'd go for Advanced/Massage.