To shoot the good ol' outdoors and moving objects

What I am looking for is 1080p frames, frames per second up to 7, wide angle shooting is an option for me (not necessarily needed), and 30 to 36x zoom. All with a price range of 300 to 500 dollars. Thanks.

I have been looking at Fuji cameras and am not sure if it is the right one to be looking for. Also a lot of the web pages out there are behind the times when it comes to reviewing a camera (2 plus years).