For learning to change chords smoothly try the 'basic' progression in different keys - C Am F G G7 , then G Em C D D7 , and so on ! When you can do all the runs smoothly , playing ANY piece of music NOT requiring 'Jazz' Chords will be fairly straight forward . If a simple picking style is incorporated , this will help with co-ordination !
When you are on F and A , there are enough Barre Chords to help with getting the feel of them too !