When to use 家 vs 师 vs 员 vs 者
I'll just talk about my own understanding here.

家 says that someone is so professional and experienced, and may have reputation so that he/she can be regarded as a master or authority in his/her field, e.g. 武术家, which means a martial art master.

师 often emphasizes occupation or job, compare 画家 and 画师.

员 is usually related to staff or crew.

者 is formal, as Mike says, and also general.