There are a lot of reasonable digital cameras out there. But on the beach, sand can get into their mechanisms and jam the zoom gearing. I've had two break this way. Getting rained on while hiking is another way to lose a camera. Waterproof cameras are a solution to both of these problems. Both Fuji and Olympus have a line of cameras starting at $100.
There one got-ya with all waterproof cameras. Whether you are splashing in the surf or whitewater rafting, the camera is going to get wet. Unless you are underwater, be sure to wipe the camera lens before you take a picture. I have had a lot of photos and video clips wrecked because of a drop of water on the lens.
The Olympus Tough was easy to control and took good pictures and HD videos. The video is 720p. Mine was rated at 10 feet. I dove twenty feet deep on several occasions with no problems
If you buy a Tough I recommend getting the warranty. For no explained reason, it stopped working after a year. One morning it didn't turn on. Sam's club replaced it. But I had to mail it in. Unfortunately, I was about to go on vacation and needed an underwater camera. That is why I bought a Fuji. It was the camera Sams Club had on sale that week.
My Fuji XP 60 is rated for twenty feet. I have had it down to 30 with no problems. Like the Olympus Tough, it takes good photos and the video is 720p. Because they are small and durable, my Fuji and my Olympus are my go-to cameras.
I do find navigating through the Fuji's menu a little awkward. I have yet to find the setting that controls how often it auto focuses during a video. Unlike my Olympus Tough, it sometimes changes focus during a video clip. This is my only complaint. This mainly happens with close, indoor shots.
I recommend the warranty if you buy one. At the one year mark, it started leaking. Just a tiny bit. It was just enough moisture to cause the flash to fail. Then USB connector rusted out. Sams Club replaced the camera with no fuss. I don't know if the seal was starting to fail or a grain of sand go in the seal and damaged it one of the times I opened the camera to charge it.