The camera or cameras in the cockpit you use to capture your video can vary widely depending on the individual user. We use an odd assortment of types styles and brands to capture the footage. We have everything from HD to 4k mounted in various locations or handheld. We have in our collection Canon, GoPro, Garmin, Sony and even a few things shot on iPhone. All can record in HD or 4K so it comes down to the software you use for editing your footage.
garmin Virb Ultra 30
I use a few different mounts to attach my cameras to the aircraft and honestly I would say that it takes less than a handful to make good videos. As far as I am concerned the only mounts you really need are a couple suction cup mounts for inside, a tiedown and strut mount for the exterior. I rent the aircraft from the school where I fly so there are limits to what I can do, I also have some inspection covers with mounts on them that work great. For inside I use the suction cup mounts from GoPro.