my 02 cents
I teach my students to retract the gear as soon as a positive rate of climb is established in everything I fly single/twin/piston/turbine. Altitude = options so you want the airplane to start climbing ASAP and almost all airplanes climb much better with the gear up.
If the engine does fail in a single engine retractable you are almost always going to be better off with a wheels up landing.
One point I feel very strongly about is that students must understand that after the engine fails the insurance company just bought the airplane. A pilots only responsibility after the engine fails is to minimize the risk of injury to him/herself and the passengers. In the case of an EFATO that means immediately lowering the nose so that airspeed is maintained and then maintaining control of the aircraft so that when it hits the ground it is in a wings level, slightly nose high pitch attitude is the key to surviving.
Finally I am going to beat my drum again about the fact that approximately 80 % of all engine failures are caused by the actions or inactions of the pilot
Most engine failures can be prevented by doing all those boring unsexy preflight and in flight checks that will prevent the engine from failing or will recognize an impending failure in time to take action before the fan stops.