I have learned SO MUCH from harmonizing the descending form of the major scale, the aeolian mode, the dorian mode, and the mixolydian mode. In the DAD tuning, I start with the D Major Scale up at the 7th fret of the bass string, and move down the fingerboard to 6+, then 5–4–3–2–1–0. The basic idea is to build a chord on each bass note, using mostly the primary triads (D, G, and A or I, IV, and V). I usually like to put Em in place of the G the second time around. to give things a touch of color and to add a little variety.
Here is a 2-page pdf in waltz time with two measures on each chord. The first 16 bars of each exercise has block position chords, and the arpeggios follow below. You can make up your own arpeggios for this as well: be creative!! .