For protein classes, you could group them by functional class, e.g. structural protein, transport protein, enzyme, etc. There aren't really any formally defined classes for general proteins. Other systems of classification could be soluble protein v. membrane protein (and within membrane proteins, peripheral, integral, and transmembrane proteins). For enzymes, there is a formal set of enzyme classifications which divides enzymes into six different categories: hydrolases, ligases, lyases, transferases, isomerases, and oxidoreductases.
For carbohydrates, there are various types of classes such as monosaccharide, disaccharide, oligosaccharide, polysaccharide; reducing sugars v. non-reducing sugars, etc.
For lipids, classes would include groups such as triacylglycerols, steroids, sphingolipids, etc.
Also, I would not consider glycerol a lipid, even though it is a component of some lipids.