Your choice of profession only determines which ground combat tree you get. All space skills are available to all professions so it becomes a matter of which space skill trees you spend your points in and how you spec your bridge officers.
At the same time, don't be surprised if they decided to redesign the skill trees in the not too distant future.
certain skills give you the ability to train your officer in III-skills. but what skills you can teach depends on what class you are. as a tactical officer you'll be able to teach Fire at Will, Beam Overload, Torpedo spread, High Yield etc. etc. to your tactical bridge officers... they're all LtCmdr and Cmdr skills.
but no cruiser have any LtCmdr or Cmdr Tactical Bridge Officer Stations.
you'll be able to use their III-abilities on the ground though.
You only need to have level 9 in the appropriate skill to teach those skills to your bridge officers, and you can have level 9 in any space skill no matter which profession you are (Engineer, Tactical or Science).
Engineering, Tactical and Science Officer are ground professions, not space professions.