The three
practical speeds are:
TAS
IAS
and
GS.
The methods of the finer points of aerodynamics as to how they are derived is done for you quite nicely by the software and hardware on modern aircraft. Let the aerodynamic engineers concern themselves with other then the foregoing three.
At altitude Mach becomes important but it is a functional form of IAS that accounts for compression.
All three (four) speeds are very important and can be significantly different.
To properly control the airplane below the altitude where Mach supercedes IAS, then IAS is paramount.
Without TAS you don't know how fast you are going through the air. That makes a big different for takeoff and landing performance at higher elevation airports (as well as high density altitudes).
Without GS you don't know when you're going to get to wherever you are going.
