You'll have many different opinions on this. The quads like DJI F-450 are perfect for the Gopro cameras. They offer better flight times, because of using only four motors and can carry the Gopro without a problem. You'll have to match good motors, good props, esc, and a decent battery to achieve the right weight/flight time, performance that you want.
You may want a gimbal to keep your video stable. I attached the Gopro to the bottom center of my F-450 quad with Avrotor 2814/11s motors, 30 amp Electronic Speed Controller (ESC) and a (overkill...) 6000 mah lipo battery. I got 9.5 minutes flight time with APC 10 inch props. I didn't have any visible vibration in my videos and because the camera was on the belly it seemed to provide more stability in the videos.
I had to land my craft on top of a wooden cigar box because I didn't have landing gear to protect my under slung Gopro camera lol.
If you are new to this than start small and easy. The DJI F450 is a small quad rotor craft that can easily carry a Gopro camera.