Although there are many options for harmonizing minor key melodies, there are certain chord choices which are more common than others. The most common 2 5 1 progression in a minor key is made up of a 2m7b5, a 57 and a 1m7.
The 1 comes from the natural minor, the 5 comes from the harmonic minor and the 2 can be created from either scale. Shown below are two minor key 2 5 1 progressions with chord arpeggios and then improvised lines played over them using the chord tones.
Another common practice in minor keys is to have a minor triad as the I chord with a line of guide tones either above, below, or running through the chord voicing, resulting in various changes to the overall chord. In the following example, notice that only the upper guide tones are needed to create the various A minor chords.
Here is an example which uses the above guide tone line and extends it further to include all the chords. Analyze the line against the chords and then transpose it to all the other keys.