It may have occured to you that it is a little odd that when you only need one finger to play the "C" chord, I am suggesting that you use one of the weaker, less co-ordinated fingers, the ring finger.
The reason for this is simple - it allows you to change to other chords much more easily. Often you will find that playing a chord in a way that seems strange on it's own makes a lot more sense in the context of changing to other chords.
Try going back an forth from the "C" to the "F". See how, if you use your ring finger to play the "C", none of your fingers has to change positions to do the chord change - they just lift up or set back down. That's much smoother and easier than moving from one position to another.
Go back an forth between the "C" and the "F" for a minute or two. Just to get the circuits in your brain accustomed to doing that. Next we'll look at changes involving the "G7" chord.