Fourball match play: order of tee shots

Scenario: Players A and B are on team 1 and Players C and D are on team 2.

Player A makes a Par, Player B makes a double bogey, and Players C and D make bogeys.

The format is best ball so team 1 takes the hole.

On the next tee box, is it correct that Player A leads off, followed by his/her teammate, Player B. And then Team two tees off (3rd tee shot and 4th tee shot).

My friends and I were unsure how to proceed when playing four ball.

Yes that is correct. Player bs score and one of the other players scores are completely irrelevant. Only the par and the first bogey matter as the team scores.

And it is players A & B choice which order they tee off, A can go first or B can go first, doesn't matter which person on the team won the previous hole. Likewise C & D can play in whatever order they like.

Just to be correct, the format, as you describe it, is Fourball.  Best ball is where one player plays against the better ball of two players, or the best ball of 3 players.

As others have said:

b . Order of Play

Answered already,  but it's simple to remember.  The honour goes to a side as an entity just as it would go to a single player.

Better ball match play - the side that wins the hole has the honour

Better ball stroke play - the side that has the lower counting score has the honour

Stableford better ball - the side with the lower net counting score has the honour.