I am a songwriter and I'm trying to learn song arrangement and how best to voice chords for my vocal melody part. What considerations should I make when choosing a chord voicing for my melody? For example should some of the notes of the melody be distant from the notes I play on the piano? I am supposing that if the melody uses chord tones then it might not make a difference but if I sing a minor 2nd or major 7th then perhaps choosing a voicing where those notes appear in different octaves might be better. Again, I am just supposing but in general there must be some consideration what voicing to use so that some notes don't clash or simply sound better.
First of all, the voice, being a completely different timbre from the piano allows you much more freedom. For melodic notes that are chord tones, you can pretty much sing in any register, as you noted.
I am assuming that the melody non-chord intervals discussed below are all relative to the root, and I am only giving general guidelines for what sounds good to my ear. Others will have their own opinions!
Minor 2nds - Only as a changing tone, hopefully with the minor 2nd heard as a chord tone in the previous chord. The current harmony would best work as a 7th chord and really should be higher, really functioning as a minor 9th.
Major 2nds - Register doesn't matter. These can be used as changing, passing or even anticipation tones in chords with a major 3rd. For chords with a minor 3rd, changing and passing tones are fine, but anticipation tones work best as a Major 9th, and may even be sustained in that register.
Minor 3rds - Against chords with a major 3rd, this will sound 'bluesy' and better when played higher than the major 3rd. Against a 7th chord, this will result in an augmented 9th.
Major 3rds - Against a minor chord, probably not a good idea!
Perfect 4ths - Like Major 2nds, good in any register as passing, changing and anticipation notes.
Augmented 4ths - As a melody note, since it is a Major 7th relative to the fifth, this is usually best above the fifth of the chord. Same as the Diminished 5th, of course.
Minor 6ths - Best as a changing or passing tone on top of minor or dominant 7th chords.
EDIT: Minor 6ths seem to work on major triads as well if a changing or passing tone. If approached upward from the fifth, I'd say jumping to a chord tone above sounds acceptable as well.
Major 6ths - Like Major 2nds and perfect 4ths, can be changing, passing or auxiliary tones in any register.
Minor 7ths - Work well with anything in all registers except chords with Major 7ths.
Major 7ths - Works well with all chords with Major 3rds and no Minor 7th, but best above the root.