I use an Olympus Tough(model TG-810) for my work, also for random shots when out and about.
Pocket size, shockproof to circa 2m, (droppable, not photo subject!), crushproof to 100kg, waterproof to circa 10m (photos in the rain or underwater), 5X wide optical zoom (28mm-140mm), GPS and electronic compass. 720p HD movies. Automatic or user controllable, whichever you like. ISO range, I keep mine permanently on exposure compensation: take it out of pocket, switch on, click, put it away: all done in a minute or so. (There is a slight delay between clicking the button and the photo being taken but I've got used to that: I don't move the camera until I sense it's captured the image. Battery life I find very good. Depending on the size of card, I get around 100 pics, or about 15 mis of video.
The model I have has been superceded. I bought it 26 May 2011 and still going strong: if and when it goes wrong then I'll get another new model without hesitation. More info here:
https://www.olympus.co.uk/site/en/c/cameras/tough/index.html