Personally, usually, I use as my point&shoot, video camera, voice recorder, GPS, . . . .oh, you see it coming. . . my smart phone.
But on a Grand Canyon white-water rafting trip, I let an uber-serious photog friend do all the research and then got what he got (well, he got three cameras, but for a on-the-water, in-the-rain, more-than-point-and-shoot) a Pentax Optio W60 which it waterproof (to 10 feet / 3m I think), 10 megapixels, 5mm-25mm, drop-resistent, and has a flash and a ton of modes and features (timer, video, delay, various focusing and lighting options, etc). $150ish, I think.
That was 4 years ago, so that same camera is now probably even cheaper on ebay, or the newest version has even more features.
I brought a solar panel, invertor, charger, and offered everyone charging for their devices. I'd never do that BPing, and I wish I hadn't on the raft trip. Babysitting a solar camera is tedious and it takes quite a while to charge the battery. Since then, I've gotten on ebay, found a Taiwan seller of aftermarket (pre-market?) batteries for the camera and ordered a handful. They are $1-$2 each, often with free shipping so it is MUCH cheaper and lighter to carry 2 or 3 extra batteries than to carry a solar charger. On a super long trip, you could mail another one to yourself every few weeks.
P.S. if you take photographs as if you're shooting film (i.e. the 3 to 6 best shots each day), your digital camera battery will last, oh, about 1000 miles. If you practice the "Mongolian Horde Principle" of taking hundreds of shots each day, then you can need more batteries and memory cards.