Cap'm is in the right ballpark. For dedicated outdoor still cameras, the market is pretty much split between Olympus and Pentax, and has been for about fifteen years. Pentax has always set up their pocket camera format a bit wider, more of a panorama, actually matching the aspect ratio of a phone-camera, while Olympus has always duplicated the format of standard cameras.
The Fuji is a good lower-cost alternative.
Photography is part of my profession, and goes way back to shooting film. I always shot Canon on film, my boss always shot Pentax on film. When digital SLR arrived, Nikon and Olympus led the market, my office went with Olympus. I've stuck with Olympus digitals because I'm familiar with their software.
A good outdoor camera should let you simply aim for about a second, be a minor or, better, no distraction from what you're doing and of course be abuse-proof. Should be on a lanyard so you just take it out of your pocket, snap it without really framing anything, drop it and forget it. The software is important, because later at home, you should rotate and crop out the photo, adjust the light, and resize down to BB format, to make it presentable. Really, none of my outdoor photos have ever been framed, just aimed and dealt with later.
My first shirt pocket cameras were Olympus Stylus bought as factory refurbs from Olympus for around $100. Each of my daughters ended up with one of those. I still have my old Stylus 850 SW from eleven years ago, it's been through a lot, taken most of my photos posted on the forums, still works and is reasonably weatherproof, can't read the icons on the program wheel anymore, but the 11-year-old factory-refurb seals finally started leaking when submerged. It was always short on batteries, but took a lot of great photos, including very good macros. I replaced it when it began to leak for trout in the classroom submerged shots. The Fuji Finepix Cap'm linked is a virtual copy of the 850 SW.
these are all from the 11-y-o shirt pocket 850 SW, along with the lion's share of archived photos I post here and other places.
The TG-5 was a birthday present to me last summer and, of course, includes every new photo I've posted since then.