A belated welcome to PF Annie.
I've had 5 different Pentax DSLR models and they have all offered robustness, very good image quality and great value for money. For your intended uses (climbing, hiking, landscapes), the KP is a good choice. It is solidly built but still compact and light weight (for a DSLR). Its dynamic range is good and it is capable of producing images with rich colours and good detail. It has an excellent feature set. The K-70 has many of the same features, but I'd suggest springing for the KP particularly because of its mag alloy chassis.
As for lenses, we tend to obsess about the differences, but any of those mentioned (e.g. Sigma 10-20, Pentax DA 12-24, DA 15 Limited, DA 20-40 Ltd, DA 16-50, DA 16-85, DA 18-135, DA 55-300) would be capable of producing good quality images. I agree that you don't really need the weight and bulk of an f2.8 lens like the 16-50 for landscapes, as you would generally be shooting at narrow apertures anyway.
The first question IMO is whether you prefer the convenience of a wide-ranging WR zoom like the DA 16-85 or DA 18-135 or are prepared to make the lens changes required with prime lenses (e.g. DA 15 Limited, DA 35 f2.4, DA 50 f1.8, DA 70 Limited) or a shorter range zoom (e.g. DA 20-40 Limited). The Limited lenses are quite compact and light weight, have excellent build quality and offer something special in image quality - they are a unique Pentax feature - but they would involve a lot more lens changes. If you carry say a 15, 20-40 and 70, the weight would be much the same as carrying a 16-85 and the cost would be significantly higher. I'd suggest that you start with a 16-85 and complement it later with a prime or two or another zoom (maybe a wide zoom like the DA 12-24 or Sigma 10-20) when you see what suits you.
If I may add two suggestions, especially about shots in the lovely dark deep woods. First, take a tripod if possible - for light weight consider a compact travel one like the Sirui T-025SK. Even something as basic as a Gorillapod makes a difference. You just cannot rely on shooting handheld to get those milky shots of waterfalls or for using the slow shutter speeds required in low light. The KP is good for high ISO shots but you will generally get much better results in landscapes with longer exposures and lower ISO than shooting handheld with high ISO.
Second, shoot RAW even if you also shoot jpg. That will at least give you the option of processing the better shots later. Yes there is a learning curve with post-processing software but even some basic adjustments of exposures can make a big difference. Here's an example. This is a shot out of camera (with the KP and DA 15 Ltd on a tripod), converted from the RAW file with no processing.
Here is the same shot after some mild processing of the RAW file (mainly adjusting the exposures in different parts of the image):
Admittedly if I had shot RAW + jpg rather than just RAW, the out-of-camera jpg would have been better than the straight converted shot above, but there is no way the camera would have made the exposure adjustments I could make easily with software to get the second image.
Shots in the lovely dark deep woods are the very sorts of shots for which you want to shoot on a tripod and shoot in RAW format. Otherwise you might as well leave the camera at home and just use your phone.