Which class of organic molecules includes those whose main purpose is long-term energy storage?

Fats.

Explanation:

A fat molecule which is called a Triglyceride consists of two main components which are glycerol and 3 fatty acids. Fats are solids and oils are liquids at room temperature. They also include saturated and unsaturated fats.

Cells store energy for long-term use in the form of lipids called fats which provides insulation from the environment for plants and animals.