Answer: Chapter 10 of Exploring Theory with Practica Musica offers some help on the topic of harmonizing melodies, but let's try to go farther.

The basic principles of harmonization will lead you to major or minor chords and sometimes a dominant seventh chord when cadencing. Then there are substitutions to increase the feeling of movement, and beyond that you get into matters of color and what amounts to adding polyphonic accompaniment.

The sevenths are easiest: a V7 can almost always be substituted for a plain V to make a stronger movement. Adding a minor seventh to any major chord makes it sound like a "dominant" - a chord that very strongly moves to the one whose root is a fourth higher. If the major triad getting this treatment is not the V, then you've made a "secondary dominant," a familiar effect in popular song. And whenever the progression involves a root moving up by a fourth or down by a fifth you can similarly add the minor seventh to a minor triad, as in ii7, V, or vi7, ii, or iii7, vi, which is a minor echo of the dominant effect. Another substitute for V might be a vii dim7, which can move as the V would, but is ambiguous enough to move convincingly to almost any chord that contains one or more pitches a half-step away. A major seventh has a motionless quality that I'd describe as more coloristic than "functional," but you'll often find it works nicely on a major triad that is followed by one whose root is a fourth or fifth higher - such as I7, IV, or IV7, I.

For I and V you might substitute a sus4 or sus2. The sus chords I think of as polyphony, though tastes differ and I suppose some may see them as chords in their own right - certainly in jazz they can be self-sufficient chords that don't need to "go" anywhere. What do I mean by "polyphony"? Just that I hear a sus4 as not a chord that stands on its own, but rather as one that is going to be followed by a triad that "resolves" the suspension; to me it's a way of writing in to the harmony a contrapuntal device. A sus4 is a triad in which the middle note has temporarily been replaced by the tone a second above, a tone that traditionally would move downward to reform the triad. That suggests that a good place for a C sus4 would be just before a chord that includes E, just as C or A minor or A minor 7. You could make a general rule of following a sus4 with a chord whose root is the same or a third lower. However, it can also sound OK to "resolve" that suspension non-traditionally, moving the upper note of the second up a step, as in I sus4, IV. In the same way, the less-common sus2 "wants" to be followed by a chord whose root is a fifth higher, as in I sus2, V.

9ths I think are purely for color and here it starts to be really hard to come up with "logical" rules. I see 9ths as decorations that could work added on a V7, but beyond that it's a matter of what sounds good. To me a chord progression with a lot of indicated 9ths, 11ths, etc. sounds like the writer is just trying to include the melody in the chords; writing polyphony, in short. Let's just consider chord tones of the 9th and above to be decorative additions that don't change the original functional role of the triad: if a V7 could belong, then a V9 is a possible substitution.

The general rule, as I see it: any chord tone beyond the triad that is not serving to strengthen a movement tendency is coloristic rather than functional harmony. A minor seventh strengthens the tendency of a chord to "resolve" upward by a fourth or, in a false cadence, downward by a third. A diminished seventh chord can be used to create movement toward any of several chords, and suspension chords are also there to create a sense of movement. Exotic creations like the augmented sixth chords, the Neapolitan 6th, and the major triad on the flatted sixth (like an "N6 of V")produce movement to the dominant and can be used as substitutions for other chords that move to the dominant, such as ii. Everything else is color, sound for its own sake. Not that there's anything wrong with that.