When taking the first step in a journey, keep it simple and stick to the straight and narrow:
https://youtu.be/EqLak8XqN94
Spike Drivers Blues (John Henry) by Mississippi John Hurt. Likely the best tune I know for getting going. One chord fingering (first position G), melody easily done over the alternating bass line.
Great for everything: rhythm, melody and simple variations, both in bass line (see how he adds the occasional "B" note on 5th string 2nd fret), melody on the top three strings (mostly using open strings and 3rd fret notes) and abundant opportunities for syncopation, etc.
This simple piece contains everything you need for finger picking. Get comfortable with it and there's little you won't be able to figure out.