Rather than tying yourself in knots trying to play tunes, which the Autoharp isn't really suited for, strumming chordal accompaniment to songs and 'suggesting' the tune is what you should be aiming for, certainly early on.

You can get interesting effects by holding two bars down at once... try holding C and F down together, strum once, let go of F and strum twice - waltz time 'oom-ching-ching', repeat, then hold G and C, letting go of C this time...

The reason why it works is because the C chord is c-e-g, and the chord of F is f-a-c, so only the C strings will sound.

Sounds complicated, but is really simple!! Hah! Just experiment!