Optional but helpful would be a Braun or Rival type stick blender. The consensus among soapmakers is that Braun works well and doesn't burn out as easy as some other brands. Whatever you use, as far as equipment, must become dedicated to soapmaking only. For safety sake, label all your equipment, with a black permanent marker, to show that it is for soapmaking only, especially the lye container. Try to wear long sleeve shirts, slacks and shoes, in case the lye splashes.
Lab coats work well.
If you are concerned with what lye can do to your kitchen counter and sink, then line all working areas with old newspapers. Keeping the pitcher with the lye water in your sink is a good idea, in case it should spill. The water will eventually evaporate as the soap bars age. White coconut oil - available at health food stores or middle eastern markets. This is expensive, but you can mail order to get much lower prices.