Three and four-handed cribbage

Hello,
I have a few questions about three and four-handed cribbage.

How is scoring done when playing a match? Simply the winner gets one point and then new game starts? What if one player is skunked? Or do the remaining players continue playing?

In four-handed version, what is more common - 2 teams or 4 individuals? There aren't as many 4-way cribbage boards available for sale...

Thanks.

Variations

In 4-handed cribbage (aka partner's cribbage) you play with a partner who is on your team and sits between you and another player. In 3-handed cribbage, if you want to keep score, I would recommend 1 point for a win, 0 for a loss and 2 points for a skunk. So if you beat one, skunked one, you would get 3 points and the other players would get zero. If you want to make it more fun, you could also do 3 points for a double skunk, but those are very rare.

Three and four-handed cribbage

I have only heard of four-hand cribbage played as two teams, and have played it that way: each player is dealt 5 cards and discards one to the crib. Deal alternates between teams, with each player getting a turn at the deal. Teams peg their scores together, and the crib counts towards the team's score.
I'm looking for more multi-player rules--been playing 3-hand (5 cards dealt plus one to start the crib, each player discards one), and we're not sure how the "go" works. For example, if B calls "go" after A plays, may C continue (and maybe total 31) or must he start over from zero?