It is also nice to know what all classes and jobs are capable of because you can immediately figure out which of the moves of your current class/job can catalyze with the move your party member used, thereby increasing damage, healing efficiency, etc. but once again that info is a plus, and isn't a necessity. (I try to know as much as possible and learn things as I go along)

It's not necessary, but it'll help you get the job done more efficiently.