You can get thread-on filters or slide-in filters. The "thread on" come in sizes to match the thread diameter of your lenses. And since buying a quality filter can be expensive, you probably don't want to buy a filter for every lens diameter you own. But you can buy the filter diameter for the largest size you need and then buy "step up rings" which allows you to put a larger diameter filter on a smaller diameter lens (step-up rings tend to be very inexpensive.)
I use B+W thread-on filters (circular polarizer plus 2, 3, and 10-stop neutral density filters.)
But for landscape photography there's often a desire to darken just part of image -- e.g. bring the brightness of the sky down so that it isn't over-exposed but NOT bring down the exposure on the landscape below. For that, there are slide-in filters -- typically rectangular -- and these are clear on half the filter and tinted on the other half. You can also choose how rapidly the the filter transitions from clear to tint by selecting a "soft edge" (very gradual transition) vs. "hard edge" (still a gradual transition... but more rapid then the soft-edge version.) The "hard edge" tends to be preferred in situations where there's an obvious line between land and sky. The "soft edge" tends to be preferred in situations where you don't have a neat "line" separating the land and sky and you don't want objects in your image to have a tint suddenly appear half-way through them.
But once you invest in slide-in filters, the adapters themselves are standard (almost doesn't matter what the lens diameter is) and you get adapter rings for each lens thread diameter you need. This makes the slide-in filters somewhat more adaptable and for this reason they are even desirable for filters that don't require a graduated tint. You can get square slide-in ND filters, and even circular polarizers. Lee filters is a big name in this type of filter system.
Overall, my biggest factor in choosing a filter is it's reflectivity. I want filters with minimum reflectivity (good quality anti-reflective coatings). This is because a cheaper filter will get a reflection in them which gives you a "ghost" of objects in your scene.