Within the wool family, you have many types of sheep, such as Merino and Blueface Leicester, which are very different from each other.
Merino wool is valued for its softness, elasticitsy and warmth. It can be stretched out quite a bit but still remember its shape it was blocked to. It is usually not itchy, making it a popular choice for socks. You can also use it for sweaters, hats, and blankets.
However it is not the strongest fiber, and can pill quite a bit but blends with nylon or acrylic can give it that extra strength and prevent heavy pilling. And it is important to note that while it has good memory, it doesn't have the best drape (the more memory a fiber has, the less drape it gets). A blend with silk can give it that nice drape, as well as a lovely sheen.
Blueface Leicester on the other hand is denser and stronger. It has little memory but it makes up for it with lovely drape. This makes it really good for lace-shawls and elegant pullovers.
If you want to make something sturdy that will be going through lots of wear and possibly get dirty, focus on finding a 100% wool with multiple plies.
As mentioned at the beginning, there are many types of sheep breeds that will produce a different type of wool from each other! Merino, Blueface Leicester, Cormo, and Shetland wool are just a few of the many wool fibers on the market, with breeders still experimenting with cross-breeding or raising uncommon species to produce new yarns.
The first thing to know about alpaca is that it is much warmer than wool, so keep that in mind when you want to knit up something heavy, like a cabled pullover. However it is lighter in weight, soft to the touch (especially if it is baby alpaca!), not terribly itchy, if at all and it is hypoallergenic. It is a very luxurious yarn that provides a nice amount of drape.
Because alpaca yarn knit up in plain stockinette can reveal irregularities in the stitches, even after blocking - something that wool is able to hide - textured stitches are usually a good way around that. Cable stitches also works, but take note that cables are usually heavy and dense and pairing it with an already heavy and dense fiber that doesn't hold a lot of memory may result in a garment that droops unflatteringly and pulls itself out of shape. But to fix that, just find an alpaca/wool blend. The wool will help it keep its shape better.
Cotton is a plant-based fiber, and as plant-based fibers go, it is best suited for warmer climates or seasons, making it a popular fiber for the summer season. It is very strong, and stronger when wet! It is generally comfortable to wear depending on how tightly it has been spun up. Tighter spins result in longer-lasting yarn but not as comfortable to wear, whereas looser spun cotton will produce a softer yarn but one that will pill and deteriorate faster. Textured stitches work very nicely in cotton.
The biggest drawbacks of cotton is that is inelastic and that it has no memory. To fix this, find a blend with wool.
It is highly recommended to subject cotton swatches to the "gravity test" to see how the swatch reacts to gravity pulling it down (usually by hanging the swatch up for about a day). Of course a bigger garment will be heavier and thus gravity will have a greater affect on it, so keep the projects on the lighter side when using cotton.
Like cotton, linen is a plant-based fiber, making it best suited for the summer. It is also inelastic and what ever imperfections you have in the knitting, it will stay "frozen in time" even after blocking, so take care your gauge remains consistent throughout! However it is even stronger and more durable than cotton and has an incredible drape and shine. It would work very well as a summer top with lots of positive ease or as a summer lace shawl.
Like Blueface Leicester, silk has lots of drape and shine. It fact, it is the master at drape and shine and is incredibly luxurious. But like linen, any irregularities you have in your knitting will show up. However, it is perfect for lace shawls. If you want to make something that would hug the body, again find a wool blend, preferably merino wool.