The makeup of a major chord is the 1, 3, and 5 notes of the major scale, as you say.
The common chord progression for most bluegrass music consists of the chords for the first, 4th, and fifth notes of the key the song is written in, the 1-4-5.
So, for the key of G, a G major chord would be the NOTES G, B, D. For a song in the key of G, the primary CHORDS would be G, C, D in major form. Songs in G will often contain other chords beside the 1-4-5, but they will USUALLY (but not always) be minor, so a song in G may also contain the Am, Bm, and Em chords as well. And sometimes a flatted 7th (F), but that's another story altogether...