What is better for plywood - varnish or paint

If you were to paint the surface it would cover and look more uniform than if you were to try and re-stain. Re-staining is more labor intensive in that unless you know the stain color it is hard to get a perfect match.

Without a picture to judge what is currently on the surface the best way to apply a paint coat is to start sanding. Hand or orbital (or both). Start with 80 grit and work through to 120. Be aware that this is most likely a veneered table top which may have only a thin layer of wood grain. If you sand through it you will expose a core or wood ply that may look different. Paint will cover this under layer but be aware. Use any paint type you prefer. An oil based paint will dry harder than other latex paints, but is harder to work with. Apply several coats.

If the stain color is even and no re-staining is required you could give it a light sanding with a 220 grit paper, wipe the dust off with a dampened rag of paint thinner, let dry and apply several coats of polyurethane (oil or water based, gloss, semi-, or matte finish).

Be aware that while you can varnish over paint it (in my opinion) will not look good. The varnish will give a light toned paint a red hue. Painting over a varnish is possible ,too. You must apply a de-glosser to the entire suface first. This allows the paint to adhere better to the surface.