1. Shop for trainers during the very end of the season / start of the playoffs, definitely NOT during the week after the draft
2. Advanced (level 4) trainers are fine unless you're working on super high end prospects (for NT/U21)
3. Youth trainers are only valuable if you have 18 or 19yo trainees -- best if you can used them for a brand new full batch of trainees -- if you only have 1 U19 and the rest of your trainees are older, the benefit doesn't really justify the cost
4. Doctors are basically insurance plans or the specialty. Taping Injuries only gives a 15% chance of an in-game return for an injury that was a single game injury, so not super high value. I'm only running a level 2 doctor for the Massage specialty, would only run higher if I had an active U21/NT player to protect.
5. Personally, I run a minimal (level 1) PR manager unless I'm using one of the two specialties for contention purposes in which case I'll use a level 2.
Overall, it's worth paying attention to how much signing bonus you're paying compared to the weekly salary -- weekly salary will increase by 1% per week for minimal staff up to 2.5% per week for world-renowned (level 7) staff. Personally, I try to churn my next trainer every 1.5-2 seasons, such that the salary savings I get from the lower weekly salary pay back the signing bonus within 10-14 weeks. Right now my staff salaries are at the low end of the cycle because all of my staff have been refreshed within the past 5 weeks.