What is the best finish....., polyurethane, tung oil, or varnish.

You may be overwatering it. They do not like to sit in water. Is it getting enough sun? Bright filtered light is perfect. I have cut the stems without leaves into 6-8" sections, rooted them in water(water level should be up past the first leaf junction) then planted them to start new plants Putting several of the newly rooted sections together in one pot will help get a fuller plant sooner..

A good coat of poly will protect it best if it's used a lot.

Polyurethane is the go-to for super protection. But poly is not the best for akll situations. http://www.diynetwork.com/how-to/skills-and-know-how/painting/whats-the-difference-between-polyurethane-varnish-shellac-and-lacquer

Tung oil is generally for raw unfinished wood. It soaks into the grain to protect the surface and gives it some color. Varnish can be used on raw or stained wood and provides a surface protection. It will give raw wood an orange tinge and slightly darken stained wood. Tends to yellow more over time. Polyurethane can be used on raw or stained wood. Water based is easy to put on and provides a clear finish that does not yellow. Oil based will yellow over time. Every one prefers water based poly for ease of application and a clear non yellowing finish. At least three coats of polyurethane for the best protection.

If the table is an antique use tung oil.