The first thing I recommend when filming from a boat is to stay dry!
There are many things to consider when filming on the water: What is the subject matter, what camera are you using, what are the conditions i.e. rain and wind, do you want to get underwater shots, do you need sound?
I filmed and directed 7 seasons of our doc-drama series called Dark Waters of Crime. For all the scenes on or in the water I used a Canon 5D mkII in an Ikelite underwater housing. Even above the water I never had to worry about rain or spray from the boat, but there are always risks. For many scenes I used a tripod rigged to a Hobie Outback kayak. It is great because it has a pedal drive system so I don’t have to paddle. That leaves my hands free for operating the camera.
In one episode of our series I had to film a dead body being recovered from a submerged pickup truck. When prepping my underwater housing, I missed securing one of the latches. I called “action” and dove into the pool. To my horror I saw bubbles rising from the housing and immediately surfaced to pass the rig to my assistant. Within minutes the crew had the camera disassembled, towel dried and packed in bags of rice. 7 days later the camera was dry and working again!
So, before filming on the water here are a few things to consider. If you are filming with a DSLR and have a higher budget you should look into a true underwater housing. I like Ikelite housings (http://www.ikelite.com). They make bodies all the most popular cameras and lenses and are rated for dives that are deep enough for you to need lights. But the best part is that many of their models are completely clear so you can see the camera and all the lights and switches.
A more affordable option is a splash bag from a supplier like Ewa-Marine (http://www.ewa-marine.com/index.php?id=6). These “plastic bags” are a good compromise for smaller budgets and much shallower depths. They will keep your camera protected from rain and boat spray as well as sub-surface. What they lack is functionality. You may not be able to adjust all of your settings without popping the camera out of the bag.
But at the very least a rain jacket for minimal protection from rain and boat spray. I’ve used a lot of Kata and Manfrotto jackets with great success. I chose a Manfrotto rain jacket over a polar jacket when I filmed the Yukon Quest Sled Dog Race.
http://www.ruggard.com/straps-rain-protection/rain-covers.
If you are using a smartphone I would consider a Life Proof or similar case. Although my iPhone drown in a LifeProof case the sprang a leak after less than two years of use.
For stability remember that the bigger the boat the more stable the filming will be. I recommend using a tripod that you can strap to the deck or weigh it down with sandbags or even a bag of rocks. If you want really stable shots I would recommend a gimbal. Either a self contained model like the DJI Osmo or Osmo-Mobile or something that is compatible with heavier cameras like the Zhiyun Crane 2 https://www.zhiyun-tech.com/crane2. I use this gimbal and it work great.
There is also a lot of cool stuff that can be filmed with a GoPro or a waterproof point and shoot like the Olympus TG-4 (I have one and love it) or the Nikon Coolpix S33 or Panasonic Lumix DMN-TS5 or Canon Powershot D30. If you have a choice of colours buy a bright one like red or yellow so it’s easy to find if you drop it!
Keep plenty of lens tissues and towels handy in a dry bag in case you need to dry things off. And most importantly wear a PFD!