As Kaleea indicates, finding the melody within the chords is often a function of the key. You may need to switch around quite a bit to find the key that contains the chords that hold within them the notes you want where you want them. Getting inventive with your baby finger as well as experimenting with alternate chord fingerings can also bring you good results. For me, the most versatile chords are C, G7, and Dm7. You may discover others that work better for you. Good luck!

Oh, by the way, in my own style of playing, my ring finger is nearly always the one that plays the melody - most often on the first and second strings; but sometimes wandering to the third and even to the fourth.