Body wash when used in this forum usually refers to a liquid cleanser, not a solid bar. And it usually refers to a cleanser based on synthetic detergents, not lye-based soap.
If your goal is to make lye-based soap, please just call it "soap" in this forum. "Body wash" is a super vague term here, as you can see by our posts in this thread. We've been trying to figure out your meaning, and every one of us has guessed wrong.
As far as a well-balanced soap, there are tons of recipes that will make a nice bath soap, but most recipes that I'd call "balanced" contain fats you don't have and less of the fats you want to use.
An example that's loosely based on one of my latest batches:
| Coconut Oil 76° | 15.0% |
| Sunflower high oleic | 25.0% |
| Neem Tree Oil | 20.0% |
| Lard | 40.0% |
With this recipe, I'd use a 33% lye concentration (2:1 water:lye ratio) if using a cold process method. For hot process, I'd use 25% lye concentration (3:1 water:lye ratio).
I'd suggest anywhere from 2% to 5% superfat. My personal preference is 2%, but I'd guess most soap makers would use a superfat that's more in the 5% range.
You could substitute palm oil or soy wax (hydrogenated soybean oil) for the lard. You could also include some shea butter, but I don't think it would work well to make shea the whole 40%, based on what others say about soap with a high % of nut butters. Shea is often used at 20% or less of the total fats.
The neem oil is another fat that's similar to lard, palm, soywax, and the nut butters (shea, etc.), so neem at 20% is a nice addition to soap, as long as you're okay with the odor. I wouldn't go higher than 20% neem, however.*
You could use any high-oleic (HO) oil in place of the 25% HO sunflower oil. There are many HO oils to choose from: olive, avocado, sweet almond, HO canola, HO safflower, rice bran oil, etc. You could include hemp oil as part of the 25%, although it's a low-oleic oil and also because it goes rancid fairly fast. I'd only use maybe 5% or so to minimize these issues.
If you have dry or sensitive skin, be careful with the coconut oil amount. Some people's skin can't tolerate any coconut oil in their soap. About 15% is what I normally use. Some people go as high as 30% in their regular bath bar recipes. So it's very much a personal choice. If you want more coconut oil, then investigate recipes with 80% to 100% coconut oil when made with a high superfat (around 20%).
I'd leave the jojoba entirely out of a soap recipe. There's no particular magic to using it in soap. But if you have your heart set on using it, keep the amount low -- maybe 5% of the total fats.
https://www.soapmakingforum.com/threads/100-neem-oil-soap.77969/https://www.soapmakingforum.com/threads/pine-tar-neem-oil-cp-recipe.73194/https://www.soapmakingforum.com/threads/neem-oil-accelerating-trace.79743/
