Using uppercase for the note names of all chords will yield a consistent appearance, which can be very important if a page has a lot of other text on it. The amount of visual processing can be minimized if major chords just use the latter, minor chords just use an "m", and major-minor seventh chords [sometimes called "dominant sevenths"] just use a "7". Note that the user of lowercase for the "m" helps create a consistent visual "shape" for minor chords, while the having the note name uppercase creates a visual commonality with other chords.
Use of "min" rather than "m" may be helpful if a reader might either misread a lowercase "m" as uppercase, or believe that the lowercase "m" might perhaps be a mis-transcribed uppercase one. Use of "min" makes the intention clear.
Using just a lowercase latter, or following the chord name with a dash, might be faster-to-write shorthand than the other alternatives, but I would tend to regard such usage as informal.
Incidentally, a related issue that comes up on occasion is the use of enharmonic chord names. In the song "Amazed", for example, the chord progression includes chords which a musical theorist would label as Cb and Fb (the song is in Ab major) rather than as the harmonically-distant B and E, but someone transcribing the chords for purposes of performance would likely use the latter forms. Arguably, Cb and Fb are more "correct", but if the purpose of notation is to help a musician play the right notes, the fact that B and E will likely do that better than would Cb and Fb is a pretty strong argument in favor of the latter's "correctness".