Plants prefer ammonium, nitrite and nitrate because they are ionic salts, and plants have evolved transport mechanisms to absorb them. Plants are so efficient at utilizing all three that you don't need to worry which one you provide.
But several people have suggested that ammonium is linked to algal blooms under certain conditions, and you should also be aware that the toxicity of ammonium and nitrite is many magnitudes higher than nitrate to fish and other animals.
I doubt that denitrification (nitrogen gas) will be ever be achieved by any aquarium filter. It is possible in commercial filter beds where oxygen levels are negligible and there is an artificially maintained high BOD level. In practice this would kill your fish. There have been several famous claims made in America by quacks promoting denitrification as a way of reducing nitrate. But there is no logical reason to do this, in addition to no feasibility.
It's been said several times before - filters are used to take ammonium and convert this into nitrite then nitrate. Plants and water changes reduce nitrate levels. Certain media can help to remove particulates, turbidity, dissolved organics, phosphates, iron and all manner of other things from your water. We all use slightly different stuff. A combination of pummice and Seachem Purigen is what I opt for, and this combo is quite common.