A quality primer is all you would need for either scenario, I see no reason to do as you say.

Generally, an oil based primer is used under an oil. A water based paint can also be put over an oil primer. Water based primers are not generally used under an oil.

These "rules' are more pertinent to exterior work where extreme variations of temperature and humidity are encountered. Oil paint is hard and brittle, latex is elastic and wants to move. They are bonded together and the latex, in an extreme case, can rip the oil paint underneath right off the siding!

If the existing finish on a wall is latex or oil, and of a low sheen, today's "paint and primer in one" paints can often be used directly to the wall without a primer. I would advise to only use a 100% acrylic paint though, due to its superior adhesion versus lesser paint resin blends.