When starting an authority site do you start with a micro niche in a certain category then choose another micro niche in that category and so-forth until you can rank in the "big" keywords or do you just write about anything related to the broad category you are choosing for your site?
You can't start an authority website, unless you really are an authority in the field already. Otherwise it will take time to build up your online links, reputation, social presence etc.. until Google recognizes you as an authority. I think it is better to concentrate on one website rather then spread yourself thin with multiple ones to start out.
It takes time to build an authority site. What I do is post everyday a few 250-500 word articles about the subject of the site. It takes time, but when you keep on doing this, visitors will come (at least that's how I do it).