If you have an answer that completely answers your question and it's the "best" of many such, then I believe that you should mark it as accepted to signal to the rest of the world that this answer is the one that solved your problem in the best way. If you have several answers of similar quality, but none of them completely answers your questions, you can either choose the best of them -- and comment on what additions are needed, update your question hoping to get a better answer, or, if you can put several answers together to get a single, best, complete answer, write your own answer combining all of the best parts of the incomplete answers into one and accept it after the waiting period.
The goal is, I think, to get a complete, accepted answer to every possible question, not to push points around on the table. You'd certainly want to upvote all the helpful answers whether you accept them or not. And I wouldn't create my own answer unless none of the other answers is acceptable.