Underwater photography and videography is a perfect "gadget sport", with many brands, styles and levels of equipment to choose from. It doesn't have to rely on expensive and high maintenance equipment. I started out with a basic compact Canon camera in a plastic case and some of the images on this website were taken with that camera. It's the perfect type of system for a beginner who may be using photography to improve their diving skills or sharing with family and friends.
Many of the photos on this website were taken with another compact camera, a Sony RX100. This camera has a large sensor for the compact category, can be used in fully manual mode and with external strobes. Its versatility make it great for switching between macro and wide angle subjects on a single dive, something that can't be done with many bigger cameras.
My main camera is currently a Panasonic Lumix GH5, a "mirrorless" micro-four-thirds camera. The GH5 is regarded as a "hybrid" camera and is highly capable as both a still and video camera. 
I am a big fan of NAUTICAM underwater housings. Highly dependable and robust, they are well made, ergonomic and relatively compact for travel.
Lighting is everything in underwater photography, whether by natural or artificial light. For flash photography I use INON strobes. For video I use compact Weefine LED lights. Size is important. Not only is it easier to travel with smaller equipment, it is easier to handle in and out of the water, and allows you to get close to subjects with less risk of damaging the reef, or scaring the critters away.
Aerial imagery is by DJI Inspire 1 Pro. This professional drone is able to capture cinema quality video footage and high resolution still photographs. The drone is capable of high speed and long range. Key features are its stability and smoothness and is its unrestricted 360 degree view. This has significant advantages for filming, without interference from spinning blades, landing legs or shadows. This is no toy.