#1 - Always hire (or re-hire) a good Fielding Instructor. The FI influences the development of every player in your system. THE first thing I do at season rollover is check to see if my FI is leaving or retiring. If I need a new FI I immediately add $3 mil to my coaching budget.
#2 - The secondary coaching ratings for all seem to be Patience and Discipline. Look at coaches' cards and you'll see that they don't change much, if at all, over their careers. If a guy has 32 Patience that's it, it doesn't develop. So at the minor league levels, starting at the bottom, I'll hire coaches with good or great Patience/Discipline combos, matched with high Loyalty. I'll scrub a few points off their "main" rating - Strategy, Hitting, or Pitching - to do this. I'm going to re-hire and promote them all, while their main ratings develop, because those are the ratings which do develop. If you hate Coach Hiring, and overpaying for a free agent coach, this saves you that hassle. I've had one season where I had to replace my major league 1B coach and my Rookie coaches; all the rest were rehires and promotions. This also keeps your coaching budget close to minimum.
#3 - In the majors, Bench coach is the last coach I hire unless I really like the guy I have and I have can really spare the money to pay his demand. All the minor league coaches seem to want to work their way up to major league bench, and he's probably the one coach who has the least impact on your franchise for the most money. If you wait till the end of Hiring - second last cycle to be safe - you can find a decent enough free agent who'll take whatever money you have left just to get a job.
#4 - An exception in the majors is if you are competing for a max level free agent player. If it comes down to tiebreakers the player might look at your coaching staff as part of his decision, in which case you want coaches with the highest hitting or pitching ratings to support him. I've heard of an owner who claimed to overpay an excellent PC to be his Bullpen Coach just to go after a specific FA. That's an extreme example.
#5 - All of this while keeping in mind that you don't want to go to the end of coach hiring and have the AI make decisions for you. Sometimes you see things on abandoned teams like terrible FIs being hired, then their prospects don't develop until another owner takes over and fixes it. Having mediocre coaches at any level isn't going to hurt your franchise, but inappropriately poor ones will set you back.