Why did we choose the key of G after C? The note 'g' is five notes above the 'c' - a fifth. The 'circle of fifths' is a system, where each successive step gets one more sharp (#). C had none, G has 1 sharp. In our next lesson we will learn the key of D - a fifth above G, and this key has 2 sharps, and so on.
The main chords of G are I, IV and V (1, 4 and 5), which are G, C and D7. Here are these chords in other voicings.
Exercise: play 'My bonny' in G, with these voicings in the left hand, and the melody with the right hand.
We play it in C and at a certain point we want to go to G. There is one chord that 'wants to go to' G and that is D(7). That is because D7 is the 5th degree of G.