I’d suggest start with some simple and always useful 1/4" and 1/8" spiral upcut like the carbide 201 and 102 and then buy chamfer, compression, ballnose or whatever else as your projects actually need them.
If you want to get clean cuts on the top surface of woods, especially things with veneered faces like MDF or ply then yes, you’d want a downcut at the top surface, but not at the bottom (opposite problem) and not for the initial cuts as you want chips to come up out of the cut.
Using a compression or downcut for a light finishing pass makes a lot of sense though, I keep a Yonico 3310-SC (cheap on Amazon) for finishing passes on birch ply. (a compression cutter has upcut at the bottom and downcut at the top but needs to be run deep in the material to work, at least deeper than the upcut portion).
If you are cutting through down cuts leave less fuzz on the top. Since the project is setting on the spoil board you get less fuzzies on the bottom but they are still possible. Depending on your hold down method down force will not try to lift the work. There is a place for both up and down cut bits.
As Liam said plastics seem to work best with single cutter bits.