Myth: If you drink coffee, your cholesterol levels will go up.
Fact: Coffee contains a compound called "cafestol" which potentially stimulates LDL cholesterol, but the compound is only found in the oil of coffee. If you make your coffee with a paper filter, you eliminate this problem.
However, if you don't have LDL cholesterol problems currently, then there is no need to worry about it.
Making your coffee with a mesh filter or by way of something like a French Press will not filter out the coffee oils.