Merle Haggard's "I Think I'll Just Stay Here And Drink" is a great example of a 3 chord country music progression. It's typically done in the key of A Major and consists of A Major, D7, and E7.
This is a great progression to practice improvising over because it lends itself to the use of multiple different scales including A Major, A Mixolydian, and A Blues scale.
With this type of bluesy sound, the tonic (A Major) could also be played as dominant (A7). Let's see what that looks and sounds like here with a progression of all 7th chords.