What birth-sign is best for an archer, who also switches it out for some unarmed combat once in a while? He doesn't focus on sneak, however.

Skyrim doesn't use birth-signs.

If you're talking about skill trees, archery is always good to go but if you're an archer you might want to invest in heavy armor because there is a perk for unarmed combat in that tree when you wear heavy "gloves".

Sagittarius

If you mean Standing Stones, I'd go with whichever one covers the most skills your archer uses. If that's combat skills and not thief skills, I'd go with the Warrior. Or use the Lover, which covers all skills.

Lover's Stone outside Markarth is a good one. I always use it.

But yeah no birth signs.

If your talking Race, use Khajitt. their claws get unarmed damage rating.

I've heard Capricorn is better. dunno why though.

hmmm. for a none stealth archer cant go wrong with the lady. minor boost to health/stamina regen.

Theif Standing Stone. That would be a great stone as it's a stealth stone which is handy to have if you are into bows and so on.