BpPilot, I'm new to multirotors myself, but your idea sounds reasonable to me. Decent GoPro type videos under $1000 definitely. I recommend looking through multirotor videos for stuff you like and copying a system. For example, the Naza flight controller thread
has lots of builds in your range and flight videos.
There are several kit systems under 1000$, such as the DJI ones, ready to go that take great video with a GoPro.
You may be better asking in the aerial photography section, as those guys can give you more specific advice.