While it doesn't help with the wood ash, if you use conventional Sodium hydroxide,
soapcalc helps with some of the maths of soap making. I use it when I am feeling lazy, or to doublecheck calculations. Different fats and oils have a different sap value, or the amount of lye it takes to saponify it due to the unique mix of fatty acids. Back in the day when lard was the triglyceride of choice, it probably didn't matter much.
Different fats also impart certain properties into a soap. Coconut oil adds lovely fluffy lather, but is incredibly drying (though a 100% coconut oil soap with about a 20-30% superfat (waaaaaay higher than normal, but it doesn't go rancid easily like other oils) is moisturizing and can lather in seawater, it is so good at lathering)). Palm oil adds a stable lather. Olive oil is very moisturizing, but a 100% olive oil soap (also called castile) has a bit of a slimey lather. So making a bastile with mostly olive oil and some coconut oil makes it a nicer soap.
I either make my soaps with a mostly lard base, or a mostly olive oil base. Then there is some added coconut oil for lather, finished off with a small amount of a very conditioning oil (walnut, sweet almond, and grapeseed are a few examples). Fragrance either comes from essential oils, or fragrance oils (I don't really care if it isn't natural, some scents can't be had with EOs, plus they stick better).