The most common types of knitting yarns are: Wool, Mohair, Kashmiri, Alpaca, Ancora, Silk, Cotton, Linen, Acrylic, Composite, etc. Knitting yarns are usually sold in skeins or dolls in different weights and lengths.
There are yarns thinner and thicker, smooth yarns or textured yarns (they can have ribbon, tinsels or just more hairy etc.). Also, there are yarns twisted with one strand or with two strands or with four. The most expensive knitting yarns are those that are made entirely of wool, cotton, silk or some material. Most yarns consist of blends with some acrylic material which make them cheaper and in some cases softer.
To start someone with knitting, it's preferable to start with a yarn that is clean (without hairs that can get involved) and thick enough (to make it easier to use and the result to be more visible) and relatively inexpensive (that is with acrylic inside), as it is almost certain that in the first time there will also be crooked-stitches.