I think I can give you a simple summary of these speeds that will help you out.
Indicated airspeed is the most important speed for actually operating the airplane. This is read straight off the airspeed indicator. It tells you when to rotate for takeoff, when you should retract or extend flaps and landing gear, how fast to fly for short field landings, etc. All of the operational speeds for the airplane, such as stall speed, manuvering speed, and never-exceed speeds are indicated airspeeds. It also is the speed you use to fly when Air Traffic Control directs you to fly a certain speed. This is the speed that is most used by pilots to fly the airplane.
Calibrated airspeed...not so important to pilots. Think of this speed as being a mechanical error in your airspeed indicator. But, the manufacturer knew about the error when they painted the numbers on your airspeed indicator to make up for the error. That is why, it is not really important that you know or use calibrated airspeed.
Ground speed...is the aircraft speed over the ground. This is the speed used for flight planning, and how long it takes to get from point A to point B. This is important to pilots in knowing how much fuel will be needed, how far away from an airport to start descending, and maybe which direction to land (if no other wind info is available). Groundspeed is either shown on a GPS (or DME, etc.) instrument, or it must be calculated. Most aircraft today have some sort of groundspeed indicator, so calculation is not often necessary.
True airspeed is a little bit complicated. The good news is, you don't really need to use if very often. It is mostly needed to do calculations in order to determine groundspeed, which I already discussed. If you don't care about groundspeed, then there is little use in using true airspeed for anything. True airspeed is used when manufacturers talk about how fast their planes will go, because that is the actual speed you travel in a zero wind condition. They could just as well call it "no-wind groundspeed." (In case you're curious, true aispeed can be determined by a calculation using indicated airspeed corrected for altitude and non-standard outside air temperature. Also, as you may have figured out, the only difference between true airspeed and groundspeed is the wind.)
So really, all you NEED to use regularly is indicated airspeed to fly the plane, and groundspeed to know how long it will take to get where you're going.
Good luck to you.