Some work better as a soap oil than others. Mineral oil is a petroleum product derived from crude oil, of which is considered to be a carcinogenic and auto-immune suppressant.
Animal fats, including lard, tend to make soap that is moisturizing, but it doesn't always have the freshest scent. If you ever get to talk to (older) people whose mom's made soap back on the farm, they may tell you that it was harsh but worked well.
This page covers using lard, or tallow, and a variety of vegetable oils. Click on the images for a page's worth of great information:
One of the greatest things
about making soap is being able to experiment to find the best one. And knowing that each oil has benefits unlike other oils or butters. Examples of this are that canola may cut soap costs, it doesn't make the best soap all by itself. Cocoa butter as a superfat, works really well, even with a mere 3-7% of the base. Yet if you made a soap with just cocoa butter, it will get so hard after 8 hours in the mold, you may have trouble cutting it, and the bubbles would be very fine. And Castor oil, which is very emolliating, is the best oil for a shampoo bar, or for a pet shampoo bar.
From 'which oils are best for soapmaking' to finding some of those soapmaking supplies....
And suggestions of the equipment you will need to start with...