Your HC coaching style just gives you additional plays for his style that the other coaches don't have. The game planning is the same as if you hit "recommend" for everything - the AI takes your roster vs their roster into account as well as your own play success to choose which plays to use, but there is minimal difference to the underlying gameplanning code. This will hopefully change in the future, but it is a lower priority to a few other things; so yeah, at this point I don't know that you should spend a ton of time worrying about your HC coaching style in a roster-only league.

OP seemed straight forward: What kind of O would be run, Balanced or West Coast?

Only roles I know of is this: HC= determines what plays you will call on offense and defense as far as playbook schemes. I do not know what value the OC and DC has. And the rest of the positional coaches determine how fast the players in the respective positions progress. For example, a QB coach with a high accuracy rating will allow the QB to progress faster in that department, etc.