A great song to start with is Skynyrd's "Simple Man". It's basically just an Open C chord (Major), Open G chord (Major) and an Open Am chord (minor) with a simple picking technique. The song begins with an open A string (fifth string up from the bottom, or high e string) then up 2 frets (B note) on the same string (use your middle finger), then up one more fret (the third fret) (C note) on the same string (use your ring finger and then form the open C chord and pick the notes). Playing These single notes are often referred to as "Bass notes" and are commonly used in many songs.
Whether you prefer fingerpicking or using a pick (both techniques have advantages) I would recommend learning and playing both ways early on to adapt your skills equally. Both take skill and a lot of practice to master.
When it comes to fingerpicking, study a technique called "Travis picking" If the song "Dust in the Wind" by Kansas, for instance, floats your boat.
