The usual choice for heat sinks seems aluminum because it has low weight, good price and thermal conductivity. Also the ease of manufacturing and availability play a role. There are another options, like copper or why not 24K gold!
The specifications about heat sinks should come in degrees of temperature resistance per watt of power. The TR specification stands for thermal resistance. If the calculations provide that the particular component would go to 5 watts and the maximum temperature is 100ºC, the heat sink must have a certain thermal resistance to avoid the threshold of destruction.
The usual parts that carry heat sinks are semiconductor devices, up to the microprocessor or LEDs. The thermal paste ensures a good transmission of heat, difficult without it due to the eventual presence of air between the pieces.