For those that don't know, TIM = Thermal Interface Material.
There are different kinds of TIM, but not like your thinking. The original performance TIMs contained silver. Silver has excellent heat transferring abilities and works well as a TIM. Newer ones are taking advantage of carbon by adding crushed diamonds or carbon to their TIMs. They don't have a dedicated usage per se, but if you aren't dealing with a lot of heat there is little point in buying the best of the best.
You clean the old stuff off by using rubbing alcohol. Use a Q-Tip for any hard to reach places. You actually need very little when you put more on. How much and how to apply depends on the type of heatsink, who made the TIM, and who you ask. I'd follow the directions on the sink/TIM.