You can get decent video with a head mount or a mask mount.
You can buy an independent head mount strap or a mask with a dedicated mount on it.
It is very convenient to have your hands free during a dive, but the video will be shaky if you do not try hard to control your head motion. You can learn to do it, and you need to be calm. You need to move your head slowly and pan like a zombie, it is really somewhat unnatural.
As soon as you get distracted, or you forget you are filming or get nervous, then your head starts darting around and the video has diminished quality for that segment. You also have to stare at things and also get inordinately close to your buddy and stare at him stupidly to capture decent video, so it is best to warn your buddy that you may be "in their face" from time to time. If I am sleep deprived, I notice my diminished ability to control head motions. Also if you want to show something very close to you and/or something in your hands like an spg or computer, you have to remember to look way down, more than you would naturally. You have to remember that the gopro is a wide (or very wide) angle camera so the subject looks much further away than it actually is, that is why you have to get your nose right into some subjects to get decent video - not so good for filming moray eels.
Edit: You also need to pause and stare at the subject with a motionless head, much longer than feels normal. With a hand held camera, you can keep the camera pointed motionless at the subject while you glance away and observe other activities or subjects that are outside of the field of view of the camera, and better plan the next shot or how you might pan. With a head mount, that option is eliminated and you must resist the temptation to do it, you need to just keep filming (staring at) the subject longer than you think you need to. It is unnatural. You can practice this by walking around the house and filming stuff and then reviewing the video. You learn to move your eyes, not your neck. This also makes it challenging to keep an eye on your buddy, because normally you just take a quick glance in their direction every 15 seconds, just to confirm their distance, direction of travel etc. You become a worse buddy with the camera on your head, unless they are your primary subject.
You want to keep the front of the camera lense coplanar with your dive mask in order to capture the best field of view - and you may have to check that angle by feel during the dive and especially after entering the water, with say a back roll. You can ask you buddy before entry if the camera is aligned on your head properly (coplanar) by having him look at the side of your head. Then you have to learn to put a finger behind the camera mount and "feel" exactly what that flat angle is by touch. If you want to film a bunch of stuff that you are manipulating with your hands, then it often makes sense to temporarily adjust the camera angle downward a little, but then you have to remember to readjust afterwards. You can also train yourself somewhat by wearing the mask and camera (and hood) in the bathroom mirror and making sure the camera angle is flat and matches your mask, this means you have to be precise with the way you wear and adjust the head mount straps, if you go that route.
I've found that hand held video can be even worse, especially if someone tries to hold the camera by itself or mounted on a wrist or a short handle. It is just so hard to control with one hand. I have had much better luck with a two handed mount that has a little mass to it to provide stability, so filming decent stuff ends up occupying both hands for me. A longer pole/stick works decent as well because of the mass and I guess it is just natural to be able to control that type of tool.
I'm not sure I would trust a stick on go pro mount to a mask frame, but I have never tried one.
