I make cold process lye soap and hot process shampoo bars. This batch I used sunflower, jojoba, coconut, castor oil with no essential oil. This one thickened up on me really fast and I had to get it in the mold without essentially oil. It's alright, it still cleans. I also make my own beard oil and we use oils with our herbs (apothecary) so each batch of soap depends on what oil we have the most of (using soapcalc).
I can't really say we have a favorite. I make a batch every year and a half or so. With only three of us left in the house it takes a long time to use a batch. We have four daughters and used to use a lot more soap. We enjoy the "old world" type skills and doing stuff for ourselves as chemical free as we can. .