Then again, I was taught to slow down on the gears. Thats all wrong now.
Not wrong, just out of date.
The system of driving taught in Britain was developed in the early thirties when brakes on car were inefficient at best. So, you needed to slow down using engine braking, which in lots of cases was more effective, reliable and often quicker than using the brakes on their own. This is not the case with modern cars! And what would you rather replace; clutches and gearboxes or brake linings?
As for the original question, if stationary for any length of time, then the handbrake should be on. Doesn't matter if it's an auto or manual. And being in neutral is probably a good idea; autos do creep so there's always
some strain on the gearbox, and holding the clutch down on a manual doesn't do the release bearing, cable/hydraulics and the fingers in the clutch cover any good.
Also, if you're stopped to turn across any traffic, make sure the front wheels are straight!