Is a sealant needed in addition to caulking

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.

The first thing you'll want to make sure to do is remove all of the old caulk so you have a smooth surface to adhere to.

Next you'll have to decide which type of caulk is best for your situation, because that will determine how easy it is to remove if you get it on other surfaces.

Latex is easier to clean up but susceptible to cracking over time, and silicone is superior but can be harder to work with and can't be wiped off easily.

For a smooth bead, make sure to not cut off too much from the end of the tube. Squeeze slow and steady. If you need to go back over and smooth, you can apply a little bit of soap and water to your finger and run it along the seam.

Have some paper towels ready to wipe any surfaces where you may accidentally get caulk.

Hope that helps!