Stilton,
Best way to help is maybe to give you a typical profile in a FJ. T/O and climb are normally flown manually. No need for A/T as the throttles are left at Mil power. At the TOC the autopilot can be engaged in an alt hold and heading hold mode. A/T can be engaged to hold the current speed (although I know some FJs have selectable A/T speeds). For small turns Hdg Sel can be used, and for long track legs you can fly direct to the waypoint. At the waypoint Hdg Sel can be selected to turn towards the next waypoint, or in Hdg Hold mode the pilot flies the a/c with the stick but when released the a/c rolls wings level into Hdg Hold again.
At TOD the A/P and A/T are disconnected and the a/c flown manually for app and landing. There are some relief A/P modes that allow a certain pitch attitude to be held, and these can be used if the approach starts to get busy. A/T can be used for the landing and approach (say to maintain 250kts in busy airspace), but that is up to the pilot. Many of us prefer to use manual throttles for landing as ironically enough its a bit smoother. We don't tend to have VNAV like an airliner so there isn't a VNAV PATH option, although as more and more jets get RNAV that may change.
Auto-approach is available in some a/c, but needs specific equipment to be serviceable, and given that it saves fuel, most FJ landings are visual approaches hand flown. Hope this helps.