You may want to check out windowing functions if your MySQL version supports them...
SELECT m.member_id AS member_id,
(SUM(c.vote_value) + SUM(c.best)*10) AS total,
RANK() OVER (ORDER BY (SUM(c.vote_value) + SUM(c.best)*10)) as ranking
FROM comments c
LEFT JOIN members m ON c.author_id = m.member_id
GROUP BY c.author_id
ORDER BY total DESC;
Another possibility is this:
SELECT m.member_id AS member_id,
(SUM(c.vote_value) + SUM(c.best)*10) AS total,
(SELECT count(distinct <column you want to rank by>)
FROM comments c1
WHERE c1.author_id = m.member_id) as ranking
FROM comments c
LEFT JOIN members m ON c.author_id = m.member_id
GROUP BY c.author_id
ORDER BY total DESC;
NB: There's a lot of open questions around this, but the above two techniques are simple methods to determine rankings in general. You'll want to change the above to fit your exact need, as I'm a little fuzzy on what constitutes the rank for a member_id.