Almost any good quality paint or varnish will work. But think about what you hope to accomplish and what it will be exposed to.
Where varnish has worn away, another coat of varnish will likely still leave the wear spots visible. You could try stripping off the old coating, and then a wood stain followed by varnish. But stains may be hard to remove. Painting is likely to give the most attractive appearance.
Will you paint the granite top? Or only the wood? How much gloss do you want? Color?
The experts at a paint store should be able to make recommendations. Do you want a water borne paint? That usually limits gloss. Top of the line is two package urethane coatings such as Polane from Sherwin Williams. Two package epoxy is also very good (but not for direct sunlight). Often found in swimming pool coatings or garage floor coatings.