What profile is best for mostly free riding with some buttering and occasional park riding?
My guess would be a hybrid (rocker-camber-rocker).
There are great options in both Camber Rocker Camber and Rocker Camber Rocker for what you have described. Also consider that brands like K2 produc only variations of flat (and flat rock) and that many riders dig some of those for your description as well.
In Rocker Camber Rocker there are great boards that will do what you are looking for. The Flow Infinite is one awesome example.