If you are shopping for filters, chances are you will find a quality, multi-coated Circular Polarizer the most useful.
Shooting digital, many filters can be easily emulated either in the camera or in post-processing software. The C-Pol is an exception. There are a variety of things it can do that are difficult or impossible to do any other way. C-Pol are especially useful for scenic shots, but it doesn't stop there by any means. They also can be used for portraits, product photography and much more.
I recommend you visit Steve's website and watch the video he has posted:
https://backcountrygallery.com/how-to-use-a-polarizing-filter/Don't scrimp on a good, high quality C-Pol. It will likely be your most frequently used filter and the quality effects every image made with it. There are a number of good brands, but B+W F-Pro and XS-Pro Kaesemann might be the best value. They're very close to the top of the list for quality, but priced far below the cost of most other brands with similar quality. You can easily spend 50% to 100% more for the same or even less filter in another brand.
Both F-Pro and XS-Pro use high quality Schott glass mounted in brass frames. They both also use extra fine Kaesemann polarizing foils and are sealed for weather resistance. Current versions of both are also "High Transmissive", which means they aren't as deep gray as other C-Pol and don't "cost" as much light loss. Depending upon how they are adjusted, a standard C-Pol normally costs between approx. 1.5 and 2.25 stops of light lost to the filter. The HT filter like these two typically cost between roughly .75 and 1.5 stops.
B+W F-Pro are "standard" size frames with 8-layer multi-coatings. The slightly more expensive XS-Pro use "slim" frames and have 16-layer "Nano" multi-coatings. B+W's standard frames are actually pretty slim already, but the slimmer ones may be needed on an ultrawide lens. OTOH, slimmer filters can be a little more difficult to install and remove from lenses. 8-layer multi-coatings are very effective... but the 16-layer "Nano" are a bit more oil, dust, water and scratch resistant.
Neutral Density filters are evenly gray all over and are used to simply reduce the amount of light passing through to the camera. ND serve rather specialized purposes, such as when you want to be able to use a very slow shutter speed and/or an extra large lens aperture in bright light... when the adjustable range of the camera isn't sufficient. For still photography, usually only one or two ND filters are needed... such as a 3-stop and 6-stop filter, which can be stacked and combined for a stronger 9-stop. If shooting video, there's considerably less adjustability in the camera, so a wider range of ND filters may be needed.
There are several other types of ND filters:
Variable ND filters may be wanted for video, but most still photographers don't really need them. Variable ND filters range from expensive to ultra expensive, and even the best of them can have uneven effects. They also can cause ugly tints in images.
Graduated ND filters are sort of "old school". They're half gray, half clear, with a transition in the middle and were widely used for scenic photography back in the days of film, such as to "hold back" an overly bright sky during exposure. Typically 1, 2 and 3 stops strengths were typical. They really aren't needed with digital.... It's often easier now to simply take two shots are different exposures and then combine them later in post-processing. Or it may be possible to simply adjust a single image in post-processing. This can done much more precisely and controllably with digital, than was ever possible with film and Graduated ND filters. Grad ND filters are over-size, rectangular filters that require a specialized holder to attach to a lens. High quality, multi-coated ones and the accessories needed to use them add up to more than the cost of many lenses. They also are difficult to shade effectively with a lens hood. Besides the different strengths of Grad ND, there are "soft, medium and hard" transitions, as well as some other specialty combinations.
Center Spot ND filters are highly specialized... typically are designed for use with specific lenses to counteract strong optical vignetting. Once again, while this type of filter might be necessary with film, but is not needed with digital. In fact, today some digital cameras and post-processing software include "lens profiles" that automatically correct for optical vignetting (among other things). Even if it's still necessary to do manually, it's a pretty simple fix in image editing software.
Of all the filters available, with today's digital cameras... a good C-Pol will almost certainly be your most useful. An ND filter may be needed for certain effects in some very specific situations. Virtually no other type of filter is needed with digital photography. For videography, a wider variety of fixed-strength ND filters or a Variable ND filter might be helpful in a fair number of situations.
Another type of filter that's popular today is a Clear or UV "Protection" filter. Whether or not these are needed or even useful is widely disputed. Decide for yourself by viewing Steve's test video here:
https://www.youtube.com/watch?v=P0CLPTd6Bds (Spoiler alert: Don't expect very much "protection" from some thin piece of glass.)