What makes you think that landscape photography needs filters? Sounds to me as if you just trying to enter a genre by getting equipment. Sorry to burst that bubble.. The subject defines the genre, not the filter.
All the information can oftentimes be rather overwhelming for a start.
I bring along 3 types of filter for all my travels :
1) Neutral Density filter
2) Graduated Neutral Density filter
The first 2 IMHO the more important of the 3. This is of course dependent on the style you would employ.
Filters are not just used only for protecting the front element you know. And besides for many people, a marginal loss in IQ of using a filter is worth the trade off to minimize the chances of an expensive lens being scratched accidentally.
I'm fully with you for those 'protection filters', that's wasting money imho. A lens hood does a better job in terms of protection, since most impacts are coming from the side in an angle to the lens rim and not straight from front.
But ND, GND and CPL are necessary to achieve effects that cannot be replicated with any software.
I guess the ND, GND and CPL filters are those used in this category. I would prioritize GND and CPL, these modify only certain aspects (a bias) of the image.
Whereas the ND just darkens the entire image (unbiased) typically so that you can get a much longer exposure to blur the moving parts of the scene or shoot a nice bokeh in very strong light without reaching
the diffraction limit of your lens.