When I redid mine I used eternabond along the main top seams and dicor self leveling stuff elsewhere. The eternabond seems like a very high quality product that's pretty easy to install. The time consuming part was cleaning all the surfaces prior to applying it. Dicor is, well, what you'd expect - kinda goopy caulk but pretty easy to work with.
Edit - I don't think you need to necessarily remove anything. I didn't. I would be very careful with the plastic covers up there as they get very brittle over time. I inadvertently broke my fridge vent cover and had to replace it.