I know nobody actually cares because I'm in like the 1% that this actually hurts... the owners around 2 years of experience who have to pay the floor yet aren't established enough to have a developed arena or any sort of real income. It's such a small deal, that it's considered insignificant. But it may be harder to keep users around past that first season because of crap like this. This isn't helping the game grow at all.
I don't know that it's fair to say nobody cares. I'm sure some people don't, but I'm not one of them. All I can do is give some advice based on what I've experienced in my time in the game, and then you're free to do with it what you want. The one "rule of thumb" advice that I will give first is that if you're anywhere close to spending more on your staff than you are on players, that's an entirely unsustainable model.
With that said, I wouldn't recommend firing your trainer either unless you had no alternative at all (e.g., you're approaching the bankruptcy limit and couldn't stop the bleeding otherwise) or if his salary was extremely insane. As it is, you're barely profitable so you should probably be able to float the trainer salary for a while if other things change. I would probably consider looking at advanced once you do get the money for a replacement, though - the difference between the levels is not significant (I think it's estimated at like 4% training speed) but the cost in salary and in bidding on them is quite hefty.
As has been mentioned, the PR is almost certainly something to not invest in significantly - generally speaking any gain in attendance/merchandising is not as much as the increased salary vs. a minimal PR guy. What I personally recommend is trying to find a cheap basic PR guy (or maybe competent with a low salary) with either National Appeal or Crowd Involvement, depending on your competitive situation - if you're winning almost all of your games, the CI specialty might help swing one of the road games, while if you're going to have a terrible season, maybe NA can swing a home game or two and keep you from relegating. If you have more money and weekly profits, you can actually switch PR guys on a game-to-game or as needed basis to maximize competitiveness - spending a small amount (~6k severance + a small bid) for an improved chance of victory in a close matchup is something I like.
Doctors, honestly, are kind of big money sucks too. I've had stretches where I had almost no injuries with a competent doctor for almost a whole season, and times where I had multiple injuries quickly with a superior doctor. If you're training someone absolutely irreplaceable (U21 candidate, or a high potential guy that can't miss training pretty much ever to reach your target build), carrying a higher level doctor makes sense. I would encourage you instead to in the short term play the odds by firing the current one, and try to find a cheap level basic/competent with the taping injuries specialty. That specialty doesn't activate exceptionally often (maybe 20% or so in my recollection) but it can help.
Just remember that salaries for staff members increase weekly, and higher staff require higher raises. My trainer right now gets an extra thousand dollars every week, which is a great gig if you can get it.