Your PR Manager is responsible for arene revenue and merchandise revenue. A higher level manager will increase these two.
Your coach is responsible for the training speed of your players. The higher the level of your coach, the faster your players will improve.
It's up to you wether the 10k/week is worth it for the PR manager, does he increase your revenues with 10k or more, then it's probably a good choice. It's also advisable to watch the staff market closely. Just 10k means nothing, maybe he's a lvl 2 with a 10k salary while there's a lvl 2 with 2k salary walking around, waiting for a team to pick him up.