One interesting option is the Pentax K-3 with the 18-55mm kit lens. The camera is below your price point
For landscape this body offers: pixel shift to increase resolution (not sure how good it is but sounds interesting), weather resistant body and lens (probably the only option at this price point), No Anti-Aliasing filter over the sensor (to allow more sharpness), has an optional GPS module available to tag photos. 100% frame coverage in the viewfinder (not available on most cameras at this price), Night vision setting so your eyes don't adjust while out doing those nighttime landscape shots.
I used Pentax film cameras for landscape for many years, my brother had one of their early DSLR cameras that held up very well to backpacker travels.
Another option is the Nikon D5600 to start out. This model falls just above their entry level camera, but offers some good features for someone starting out in photography. Start out with the 18-55mm AF-P kit lens, it will work fine for landscape, mountain scapes, and is easy to carry around all day taking pictures. This kit is right at your budget, they will add the 70-300mm AF-P for another $100 in the kit. Add a $10 Rain Sleeve to use in the rain.
Used cameras are a good option, but it helps if you have some experience with cameras before jumping in and buying a used model. You might not know if the problems are operator or camera error.
Remember to add memory cards, extra batteries (cold weather shortens the battery life), tripod (about $100 for the Manfrotto Compact Advanced is about as cheap as you want to use and you can easily spend more than what your camera cost), bag. So about $200 in extras.