Turbinado Sugar
As I understand it, turbinado sugar is sugar that is spun (in a turbine or centrifuge) to remove the impurities but it is not as pure as white sugar. It has a characteristic light amber color, and a little extra taste from the residual molasses that was not spun out. Nutritionally, it is virtually identical to white sugar, but it may retain some chromium which is thought to be useful to help the body process sugars. But it doesn't have any vitamins to speak of. I like turbinado sugar but it tends to be more expensive than refined sugar without much benefit (but if it helps your conscience when you add two tsp to a cup of coffee, fine ;-).
Both beet sugar and cane sugar are sucrose, so theoretically the refined versions are identical. Certainly they can be used interchangeably in cooking.
Much fuss is made over the evils of table sugar, but in reality it's no worse than refined starch insofar as health is concerned. However, most refined white wheat flours have the minerals and vitamins of the whole grain wheat added back, at least partially, to make them "enriched", as does another pure starch, white rice. So in that respect they are better nutritionally than refined sugar. Regardless, they will spike blood sugar quicker and higher than the sucrose in table sugar, because refined starch is simply a chain of glucose molecules, which the body very quickly breaks down to separate glucose molecules, which enter the blood stream and raise blood sugar most rapidly. Sucrose, which has a more difficult glucose-fructose bond, takes longer to digest, and convert entirely into glucose for the blood.
In other words, I don't feel all that guilty about using refined table sugar to sweeten things like coffee or oatmeal. In reality the caloric value is no more than an equivalent weight of starch, which is a small amount, and we eat a lot more starch than we do sugar (or should).