With regards to killing an engine, I choose to use all three: fuel selector, mixture, and throttle.
I use the mixtures to simulate engine failure below Vr (i close the mixture pretty quick on takeoff roll, usually right before the airspeed comes alive). I NEVER simulate engine failure below 1000' AGL (just my paranoid self); unless we are in the traffic pattern (simulating failure in the pattern or single engine approachs). I use throttle below 3000'. I use Mixture and Fuel Selector above 3000'. I use the mixure when I want a clean shutdown of the engine. I use the fuel selector to catch the student off-guard (say their looking either to the left for traffic, ill kill the fuel selector and wait for it to die and see their reaction to the situation).
Of course, in all instances; im constantly aware of which engine I killed and which rudder (instinctively) to use.
With only 700tt and over 500multi (all BE76), i am very confident in a single engine situation (as ive had to land a few).
As for the POH saying youll get 100-200feet FPM climb (single engine). For the most part, i would add about 20% error to that, seeing how most of us are using aircraft dated back in the late 70's.
Oh, and for the students who arent comfortable with flying with only one engine; i show (demonstrate) them you can do steep turns with only one engine, even into the dead engine. As long as its coordinated and you watch your speed (watch that A.I.!!).
Just my 2cents on this subject.