First off, I think regarding picture quality you really can’t go wrong. Any modern camera can take excellent photos – especially of static subjects. So the main differences will be: Usability, flexibility in different lenses, flashes, etc, focus and performance in video, focus of moving subjects, how narrow a depth of field you can get, and of course price.
If you have a decent store near you, try different cameras and see how they feel and operate in your hands. Consider different sizes from a Panasonic GM5 to a G7, to a Nikon D750. You may decide that you just don’t want to lug around a big heavy camera when hiking. Or you may decide you like the feel and operation so much more that you don’t mind it. Personally, I think either you want to go really small and throw out ergonomics – basically a compact like a Sony RX100, or get something that is nice to use from a Panasonic G7 on up. I regularly hike with my Canon 70D, but also sometimes just take a little Canon S100.
Consider how it feels and operates in your hands. When I was making my decision between a Nikon D7100 or a Canon 70D, the location of the main dial was the main deciding factor. My finger doesn’t like the dial parallel to the ground in front of the shutter button on the Nikon – it much prefers the Canon placement perpendicular to the ground behind the shutter button. It may sound silly – but I’m the one using the camera, and enjoying using the camera, so I want a camera which operates well in my hands.
Regarding flexibility, Canon, Nikon and Micro-4/3 all have you covered. Lots of lenses and flashes to choose from. IMO, Canon crop lineup is the best of the three once you consider price, but I may be biased. Sony is making some great cameras, but the lenses are lacking and expensive. You don’t want a lot of lenses to start with, but if you catch the photography bug then, well… you may just buy another camera body anyway so maybe don’t worry about it.
If you are interested in video, then it is difficult to not recommend Panasonic or Sony. 4k video, downscaled to HD or not, simply looks much better. But the Canon 70D or 80D has the best focus during video – so you can “pull” focus from one subject to another when shooting.
For focus of moving subjects, DSLR is still a bit better, with Panasonic and Sony trying hard to catch up. And the more you spend the better focus ability and shots per second you will get. This may not matter too much though – I think most cameras will be pretty good unless you really want to get into bird or sports photography.
For narrow depth of field you want a big sensor and a high aperture lens and generally a longer focal length. I’m happy with a crop camera with a 1.8 aperture lens. A full frame camera would help to isolate subjects more, a micro-4/3 camera would not have quite as much flexibility.
So, after all that, I would recommend one of the below. Actually, I think you should start with just the kit lens and add on later as you decide what you need, but sometimes you’ll get a good deal in a bundle.
Panasonic G7 with 14-150, 20mm 1.7 and 42.5mm 1.7
Canon 80D with 18-135 USM (or Canon 70D with 18-135 STM or USM), 24mm 2.8 and 50mm 1.8 STM