I don't know much about filters - questions

I've seen a wide range of ND, GND, and CPF filters on various sites, each of them ranging widely in prices. As an entry level, amateur photographer, what kind of price range am I looking at for each of these? I would like to have each of these filters, but what makes the expensive ones better? Is it durability, or do they actually filter better? I don't need anything expensive, so I'd like to go the cheap route for now, so I can learn about how they can improve my pictures without the big price dent of a higher quality/more durable one that I won't need right now/

Don't go the cheap route. If you have a limited budget get fewer, rather than cheaper, ones. The price difference represents multi-coating vs. uncoated-single-coated glass. Coating reduces reflections of light, and light causes flare - an uncoated filter can reflect around 7% of the incoming light; good multi-coated filters will reflect on the order of 0.3-0.5%. This reflected light can affect your photo via loss of contrast or lens flare.

Another factor affecting the price is quality of the lens (yes, a filter's a lens; one designed to have zero impact on the image). More expensive filters have carefully-controlled surfaces so they're absolutely parallel and won't distort your image. Cheap filters may have unevenness that leads to aberrations.

So get good filters right off rather than cheap ones you'll need to replace. Good brands and lines are Heliopan's SH-PMC, B+W's MRC and Hoya's S-HMC (or better). A polarizer, when you need it, is indispensable and there's no substitute for it. By all means get one (or more, as needed) of these.

For graduated ND, get the rectangular/square ones that fit into a filter holder. I use Singh Ray graduated ND filters in the Cokin filter holders. They're pricey, but they're absolutely neutral and won't impart a colour cast to the photo.

Thanks for your help. Now to get more basic, how do filters typically attach to the lenses? You mentioned a filter holder for the non-circular filters, but what about the circular ones?

Circular filters screw onto threads in the front of the lenses; the same threads that your lens cap grips onto (they typically have threads on the front of the filter as well so you can attach the lens cap even with a filter on). Even the rectangular filter holders have a threaded adapter which screws onto the lens and snaps into the filter holder.