I've been making bath and beauty products for 11 years now, and there are some products that I just can't live without. I use these to make sugar scrubs, lotions, and soap, so they are very versatile. I'm not a big fan of clutter, so I don't buy things that only serve one purpose unless it's absolutely necessary.
heat resistant glass bowls. You'll want a variety of sizes, but make sure you have two small bowls and at least one medium bowl. Glass works best because chemicals in plastic can leech in to your recipes. Also, some ingredients can react with metal, so avoid using metal.
Stainless Steel Saucepan
Stainless steel is an affordable option that will be safe for making your natural beauty recipes. When you're shopping, look for a saucepan that will hold your 4 cup Pyrex measuring cup or a mason jar for a double boiler if you don't want to buy a separate one. Just remember not to put the glass on direct heat. I use a canning jar ring to elevate the glass.
double boiler. If you don't have one, you can make one with a heat resistant glass bowl sitting on a trivet in a medium or large saucepan. If you plan to melt beeswax or butters often, then consider a double boiler because it is easier to use.
wooden utensils because plastic can melt and leech chemicals in to your concoctions.
stick blender to blend some recipes right in the bowl. It's easier to use and easier to clean than using my stand mixer.
coffee grinder to grind nuts and other items for my recipes. I find that this is a necessary tool and works better than a food processor or blender. You may also find that a dedicated coffee grinder and blender will be helpful for other ingredients.
mortar and pestle. I just have a small one because I usually make small batches.
You don't need to buy all of these when you get started. I didn't get a double boiler until I knew that I would be making my own recipes often. You may already have some of the tools, and you can reuse them. Since you are not using chemicals, it is generally safe to use the tools you use to prepare food. Use your best judgement because some ingredients are safe for topical use but are harmful when ingested.