Sin is choosing to do wrong or to omit doing what is good?

Sin is choosing to do wrong. Unless you give in to a temptation, you haven't sinned. Sinning is the very act of saying 'yes' to the Devil/temptation.

Answer

Both. Edmund Burke (possibly!) once said "All that is necessary for the triumph of evil is that good men do nothing.". We are all sinners because we all choose to do wrong on so many occasions but also omit to do things that we should.

There is a very old prayer of confession in the Anglican Church which has these Words:

..."We have left undone those things which we ought to have done; And we have done those things which we ought not to have done; And there is no health in us."...

So sin is not simply choosing to do wrong. There are many who think that they never sin because they dever do anything wrong. But they are quite happy to walk by the collecting tin, or turn off the news when there is an appeal in Africa, or not bother to visit the elderly woman who has just lost a husband. We are all sinners and all need God's forgiveness and grace.