Since most fabric sites categorize and describe fabrics by structure first and then fiber content, we'll go ahead and make the bullet points fabric structures and then list the commonly available fiber contents. Absorbent fibers include cotton, hemp, bamboo and other rayons (viscose, acetate, Modal, Tencel), and their blends; polyester microfiber, composites like Zorb, and less common natural fibers like linen, ramie, sheep's wool, and silk. Blends of natural fibers with synthetics like polyester, acrylic, or nylon are usually okay if there is less than 20% synthetic fiber in the blend. If you don't know the fiber content of your fabric, you can do a burn test (video, chart of results at DitzyPrints), but that will not tell you the percentages of a blend. If you aren't sure whether a material is absorbent enough for diaper use, wash and test it before cutting.
- Fleece - a medium to heavy weight knit fabric with a brushed nap on one or both sides. This includes sherpa, which has a textured nap. Brushed surface is prone to pilling. It is usually a good compromise between bulk and absorbency. It is important to note that polyester or acrylic fleece is not absorbent unless it is also labeled as microfiber, and even then it may be more of a wicking material than an absorbent one. Commonly found in cotton, bamboo rayon, hemp, and blends of two or more of these three as well as with polyester or nylon.
- French terry - a light to moderately heavy weight knit fabric with flat loops on one side and a smooth knit on the other. Also often a good compromise between bulk and absorbency. The loop side may work with a Snappi or Boingos. Commonly found in cotton and cotton blends, bamboo and other rayon blends, and less commonly in hemp or linen blends.
- Interlock, rib, or jersey knit - a very light to medium knit. Interlock looks the same on both sides, as do some rib knits. Jersey looks different but still smooth on each side, and curls at the edges, including cut edges. Rib knit usually works well with a Snappi or Boingos. Knits with a high rayon content or low quality cotton may pill. Commonly found in cotton, bamboo and other rayons, hemp, silk, wool, linen, ramie, natural fiber blends, and blends of natural and synthetic fibers. It's starting to show up in microfiber as microfiber jersey sheets, which may or may not be absorbent enough for diaper use and is not recommended to be used next to the skin because of how drying it can be.
- Double and single loop terry - medium to heavy woven or light to medium knit. Double loop terry has loops on both sides, and single loop has loops on one side and the other side is smooth. Works well with a Snappi or Boingos. The loops allow for faster absorption, but add bulk, so loop terry does not hold as much for the thickness as a smoother material. Commonly found in cotton, bamboo rayon, hemp blends, microfiber, and less commonly found in linen. Microfiber terry is not recommended to be used next to the skin because of how drying it can be.
- Flannel - light to medium weight woven with a brushed nap on one or both sides. The brushed surface is prone to pilling. The light, "quilting" weight cotton flannel is the most common and takes a lot of layers to reach the needed absorbency. Diaper flannel and a lot of bedding is a heavier weight. May be more cost effective if upcycled than bought as yardage. Commonly found in cotton, bamboo rayon, wool, blends with synthetics, and rarely in hemp blends.
- Birdseye and other twills - light to heavy weight wovens with a diagonal or diamond shaped texture. Includes most diaper gauze. Usually works well with a Snappi or Boingos, but prone to snags where a thread or a few threads pull up a loop in the fabric. Traditional flat and prefold material. Commonly found in cotton, bamboo and other rayons, hemp, linen, wool, silk, and blends.
- Thermal knit or waffle weave - medium to heavy weight woven or knit with a pronounced square/pyramid texture. The knit is stretchy, and the woven often has a small amount of mechanical stretch after prewashing. Works wells with a Snappi or Boingo. Functions much like loop terry, with the same bulk problems. Commonly found in cotton, bamboo and other rayon blends, blends with synthetics, and occasionally hemp or linen.
- Composite materials - can be any weight and are usually nonwoven/fused. The most common, Zorb, is light in weight and nonwoven, and should be sandwiched between two sturdier and/or smoother fabrics because the surface is prone to pilling. Zorb 2 is already sandwiched between layers of bamboo rayon. Zorb is made from cellulose and synthetic wicking materials. Other composites may include microfiber, bamboo and other rayons, cotton, or wool components, but are much less common.
- Other wovens - can be any weight, and smooth or textured. Commonly found in cotton, linen, or bamboo and other rayons, as well as blends, and include quilting cotton, sheeting, and shirting, all of which are light weight and take a lot of layers to reach the desired absorbency. Wool is also fairly common, but wool wovens are often on the scratchy side. Less common fibers are hemp, ramie, microfiber, and silk, and less common fabrics are canvas, duck, suiting, and jacquards/fancy weaves.
- Other knits - can be any weight, and include sweater knits, double knits, and nap/pile fabrics like velour and minky. Sweater and double knits are commonly found in cotton, bamboo and other rayons, ramie, linen, silk, wool, and blends, and less commonly in hemp blends. These usually work well with a Snappi or Boingos. Velour is commonly found in cotton, bamboo and other rayons, and blends. The only absorbent type of minky is made from microfiber, and is currently milled only for Fuzzibunz.
All natural fiber fabrics should be prewashed/preshrunk before cutting unless you know exactly how much the particular fabric you are using will shrink, and are using only one fabric or fabrics that all have the same rate of shrinkage. Looser weaves and knits will generally shrink more than tighter ones. If you want to be able to launder wool with the rest of your diaper laundry, it needs to be rather firmly fulled/felted.