When I first learned fingerpicking many moons ago, I started with a D chord and used what they called a Travis pattern on the right hand. The D was easier because it limited to four strings. When I had the right hand down on D I practiced switching to a C, which moved my thumb over on a five string chord, which gave me an idea of how kewl the bass part sounds. Then practiced switching to a G. To me the best part of finger picking is playing the bass part with the thumb.
This looks similar to the pattern I learned (though I hate the whole "dummies" thing)
I remember having to play the pattern about a million times before I got it down, then had to keep the right hand going steady while changing chords. Once I had it though I could apply to any chord progression. Sounds real advanced to non-guitarist listeners!
I guess an easy practice song would be "Dust in the Wind," which sounds like an Am to C to G thing. "Helplessly Hoping" by CSN is another fingerpick classic.
Critics of learning a "pattern" say it sounds too rigid. Nowadays I mix up fingerpicking with chords to keep from sounding too same/same. But it really helped me learn to isolate and emphasize the bass strings.
Good luck, keep a pickin!