What is the appropriate type of caulking around a kitchen sink?
You need a 100% silicone clear caulk and since it is near a sink I would get something that is mold resistant.

Silicone for the sink to counter binding and its flexibility with temperature change.

Clear because you don't want to have staining issues down the road.  Also if you need to add caulk down the road - clear matches clear.  

GE Silicone II

I have used this on almost anything.