For starters, the simplest, most helpful chord progression to study could be 1, 4, 5. The first, fourth, and fifth chords in a major key are the foundations of blues, country, and rock and roll. Many pop chord progressions are also centered around these three chords.
In a major key, all three of these chords will be major. In the Nashville Number System, all numbers are assumed major unless notated otherwise.
In the key of C Major, made up of of the notes C (1), D (2), E (3), F (4), G (5), A (6), and B (7), the 1, 4, 5 chord progression consists of C Major, F Major, and G Major.
C Major
In the key of C Major, this chord is "1"
In the key of G Major, made up of the notes G (1), A (2), B (3), C (4), D (5), E (6), and F# (7), the 1, 4, 5 chord progression consists of G Major, C Major, and D Major.
G Major
In the key of G Major, this is the "1"
In the key of D Major, made up of the notes D (1), E (2), F# (3), G (4), A (5), B (6), and C# (7), the 1, 4, 5 chord progression consists of D Major, G Major, and A Major.
D Major
In the key of D Major, this chord is "1"
In the key of A Major, made up of the notes A (1), B (2), C# (3), D (4), E (5), F# (6), and G# (7), the 1, 4, 5 chord progression consists of A Major, D Major, and E Major.
A Major
In the key of A Major, this chord is "1"
Let's now look at the two most common barre chord 1 4 5 patterns. First, starting 1st chord root note on the sixth string.
G Major
In the key of G Major, this chord is "1"
Now let's look at the 1 4 5 barre chord pattern with the 1st chord root note on the fifth string.
C Major
In the key of C Major, this chord is "1"