This progression is just two chords, E and A, and if you were going to solo over this I'd stick to an E major pentatonic scale. I think that scale sounds best in the genre and it's nice and happy. My favorite part about this riff, and what really gives it a distinct sound, is the use of inversions. An inversion is simply when we take a chord tone other than the root and put that in the bass: root position is R, 3, 5, 1st inversion is 3, 5, R, and 2nd inversion is 5, R, 3. Although in this tune I'm technically playing the bass notes on the verse as open strings, my ear is really hearing the 3rd played on the adjacent string on the 11th fret for both the E and A chords. This is a very common and extremely useful to make a basic chord sound more interesting. I especially like it against open strings.
Interestingly enough, I first learned this from Black Sabbath's "War Pigs" where Iommi plays this right at the top of the tune. See? Alt country, heavy metal, blues...many connections. And, oh yeah, Black Sabbath rules. M/