Cookie cutter approaches to trimming work well for cookies.

For airplanes, it really depends on type of aircraft, type of flying you intend for it, and what your expectations are.

A normal trainer usually takes a couple flights to trim out with control centering, balance, throws, and thrust lines.

More advanced acrobatic models may take dozens of flights worth of changes, though the tendency today is just to mix out problems with computer radios, that should only be done after the other things are taken care of first.

An airplane that is well trimmed is much easier to fly and can make you appear to be a better flier.

As to CG of a model it is usually a personal preference of each flier.  For myself, I like them extremely tail heavy, as this improves certain aspects of control - but you just breathe on the sticks to manouver.

A nose heavy model will have higher takeoff and landing speeds than a model balanced further back.  Most trainer are designed to operate nose heavy, as this improves the "self righting" aspects of an airplane.  General charateristics are that the airplane climbs with more speed, and loses altitude when it slows down.  Since you pick up speed in a slight dive, the model will tend to recover back to a climb.  Properly designed and trimmed, it will soon find its stable point and be changing altitude depending on power setting.  (Assuming the pilot does nothing). 

But the positive stability of the model is reduced as the balance point moves back.  At a certain point, you reach neutral stability, and the model tends to hold a position (which is the point of doing dives, but unneccessary).

Behind this point, pitch control become divergent.  Airplanes can be flown balanced this far back, but it takes a pilot that is very skilled to survive the experience.  When the airplane starts to pitch up or down, it will do so at an increasing rate, and the pilot has to counter control to maintain level flight.  If you suspect your plane is tail heavy and you do get it in the air, it is best to get it down as soon as possible, since burning fuel usually makes it worse.