Tim Gilbert breaks down the task of singing & playing the acoustic guitar into 3 simple steps.
Step 1: Strumming
You could hold a chord, but that isn't necessary when you are getting used to the down-up strumming motion. It helps to talk along, as it will prepare your to do two things at the same time (sing & play).
Step 2: Changing chords
Try switching from G to C Ad 7th. Helps to say a word, like 'change' for instance, while switching chords. Slow down if necessary.
Step 3: Learn melody and lyrics of the song, so that you don't consciously think about this while playing.