This set of shaders right here is the most important thing you can buy. If you don't want to invest that much you can just buy Nuln Oil and Agrax Earthshade individually and be fine.

If you already have acrylic paints you can just use what you have - just make sure to thin them until they are almost as thin as milk. Thick paint will cover up detail.

You will also want Krylon Matte finish or Testor's Dullcote matte finish to seal the mini.

I recommend watching Sorastro's painting guides, his Zombicide series starts from the most basic techniques.