I never brainstorm at all, at least not in the common definition of the word, and I use new ways of doing things for practically every new project I get.
However, the way I usually start with a project, providing I haven't had a chance to see enough yet, is to look it through completely several times to get a grasp of it, and then demanding a spotting session with at least me, the composer, and the director. In some cases, also the main producer, but that's a thing between the director and the producer, and nothing that really concerns me.
I work mostly as a full-on sound designer, and as such I always have my recorder and a selection of mikes with me to record anything I might find. Often, the first thing I might try after the dialogue editing is to see which ones from the latest batch of sounds might be particularly sweet in the project I'm in at the moment. After that the road will fork in a selection of virtually billions of ways, depending on the project and my latest experiences. No matter how I go on, however, I make a first simple editing/design that I enhance as I know how much time I have left.
For me, style is rarely if ever a conscious choice. Though I do always enter a project with a direction in mind, so far I have always changed that direction many times during the course of the work as I've found new and better ways of doing things. It might sound like I'd lose time from that, but as I always work with my projects very openly and unlocked, on the contrary that actually saves a lot of time I can use to make the project even better!