the Chicago Manual of Style suggests this order:
⃰ (asterisk)
† (dagger)
‡ (double dagger)
§ (section mark)
‖ (parallels)
# (hash)
(Hard to present glyphs that would actually be used in print - I've chosen what I think is close - but they are not that close because wrong font)
Compose key shenanigans can make such typesetting significantly easier. That's built-in on Linux/X, but there are also easy solutions for Windows systems.