*Olive oil is cost effective and good for skin conditioning. It can be used singly to make Castile soap which is sought after as a very creamy, mild soap. It will harden but needs to dry for 6-12 months so it isn’t slimy.
*Castor oil is more expensive but used in smaller amount for skin conditioning, bubbles and creaminess. Normally used less than 10% to avoid sliminess (even in a harder bar). Shampoo/shaving soap have higher levels with some up to 17%. Drain well after use.
*Coconut oil hardens, bubbles, and has high cleaning properties but low skin conditioning and creaminess. Unfortunately it is expensive when pure. Buying bulk from cooking wholesalers may have added preservatives in it.
*Beef Tallow has a long history to support the claim of being the best (or best equal to Olive oil) single oil for soap making. It hardens, adds to conditioning and creaminess, and also bubbles and cleaning characteristics. It is very good for your skin. Because of the shift away from animal fats you probably can get free fat from your local butcher to render (boil down to separate the “bits” from the oil).
Rendering: Cut off the worst of the meat bits/cartilage etc, dicing then cover the bottom of the pot in water and use medium heat to get the oil to liquefy. Stir often to reduce sticking to the bottom till the chunks are browned, floating emptied of most of the oil. Strain with a fine strainer (I use a strainer and an old stocking). Shelf life is a lot shorter than many oils so I freeze or refrigerate.
*Palm Oil hardens, conditions adds to creaminess. Similar to Beef tallow in its characteristics… but it’s cheap and I don’t have to render it.
*Palm Kernel Oil hardens, bubbles and has a high cleaning characteristic. Characteristically, an alternative to Coconut oil if the price is better.
*Neem Oil: I have used this as a superfat for my doggie shampoo bar (Good for skin and an insect repellent). Maybe the dog doesn’t mind the smell. The smell does fade in time (it needs to). Makes the soap bright yellow.
There are many other oils such as Shea Butter, Cocoa Butter etc that are often used but the costs are increased.
Create a soap with the characteristics you wish by mixing these to oils. www.soapcalc lye calculator has a very good program showing the characteristics of each oil and the resulting combination characteristics. There are exceptions to this method, such as using Olive Oil for a Castile soap but when you understand these, it works well.