I usually recommend french press, it’s easy, forgiving and doesn’t require any filters or anything. Grinding-to-brew is probably the single biggest difference you can make, just getting some kind of burr grinder for yourself. Don’t need anything expensive for home use.
Electric kettle is super handy, a kitchen scale is nice for measuring, and that’s about it.
Then there’s the beans, but that’s a whole topic on its own, and isn’t really all that hard. But first things first.