There is no rule or official stance. In my opinion, you should accept the answer that either solved the problem, got you as close as possible, helped you the most, etc.
The best answers show up first so that they are always easy to find.
The above phrase should not be construed as "accepted answers show up first, and only accepted answers are best." I think this is describing the entire sorting algorithm: If a question doesn't have an accepted answer, the default sorting is by votes, with the highest-voted answer first - and those are "best" in that case. If there is an accepted answer, it sorts first, but then the remainder are sorted by votes. (With one exception: if the asker answered their own question, and accepted that, it will not sort above any answers with higher votes.)
Remember that the check-mark serves two purposes: (1) it acts as a reward to the person who best answered the question, and (2) it serves as a flag post for other users that this was the answer you chose (and, implicitly, that you implemented whatever solution it proposed).
Of course, the asker doesn't always choose the best answer (I've seen many accepted answers with a negative score), but ultimately that's at the asker's discretion. The check-mark is just one flag post; up-votes and down-votes are often more valuable because they represent a larger and more representative segment of the community.
I will advise you to not accept answers too early. I know that you only have to wait 15 minutes before you can click the check-mark, but in a lot of cases, those first couple of answers you get may not be the best answers you could potentially get. Accepting an answer too early may actually prevent you from getting better answers, because, even though you can later change your check-mark, questions with accepted answers tend to not draw any further answers (unless the accepted answer is really bad). Also keep in mind that answerers who later lose the check-mark may feel offended that you took it away. Especially when they do it 4+ times, as just happened to me. So don't feel rushed into accepting an answer quickly, and if you get bullied into accepting, please flag it.