What materials have you seen built for a poker chip? plastic, clays, ceramics..etc.
All modern poker chips are made out of plastic, even the clay chips that we love so much. Clay chips are not made out of clay, and ceramic chips are not made out of ceramic. They're made out of plastic. All of them. Every one.
There are many different
kinds of plastic, and even similar kinds of plastic have many different
formulas. This is why different chips feel very different from each other (well, one reason why, anyway).
Antique poker chips have been made out of bone, ivory, wood, paper, mother of pearl, assorted early plastics (noteworthily phenolic resins aka Bakelite, and celluloid), and "composition" or "clay composition" which was a mixture of plastic (either natural or artificial) and various materials including clay.
Is there levels of quality of a certain material?
Quality is subjective, although most PCF members have general agreement about which chips are better quality. Quality is partially determined by the formula of the chip's plastic, but is also greatly affected by the physical design of the chip (e.g. with or without an enclosed metal slug, or compression molded versus injection molded) and by the degree of care taken in the manufacturing process.
Grocery-store lightweight interlocking chips are probably made out of acrylic. Mass-market chips that are marketed as "high quality" "casino-grade" "clay composite" chips are usually made from some variety of ABS and are considered low-quality by PCF members for a number of reasons, not all of them related to the material. The chips that we consider high quality - ceramics, clays, and casino-grade plastics such as Bud Jones and Matsui - are made from unknown varieties and formulas of plastic, although we've recently learned that TR Kings were at one point made primarily from vinyl, probably meaning PVC.
Chip manufacturers have spent a lot of time adjusting their formulas, and that gives each different chip a characteristic feel. Even on the low end of the price and quality spectrum, different cheap chips will have slightly different formulas and so will feel different.