Start with mounting style, since your sink or bathtub design already decides most of this for you — deck-mounted for a standard vanity, wall-mounted if you’re opening up the walls anyway, or floor-mounted if you’ve chosen a freestanding tub. Trying to pick a finish or mechanism before settling this just means redoing the decision later.
Once mounting style is settled, prioritise finish and mechanism together rather than separately — a matte black single-lever faucet and a chrome dual-handle one solve very different problems, so decide based on how the bathroom will actually be used day to day, not just which one looks best in a photo.