As a vegetarian, I began using only soft oils and cocoa butter and shea butter initially, as they were the easiest to come by at first. Later I had the opportunity to use mango butter, a luxury in soap, that many use only in leave-on body products. There are others, even more expensive that you can experiment with as well, but I still mostly use only cocoa butter and shea butter in soap rather than the expensive butters.
The commonly recommended usage rate for butters is roughly 5-15% for cocoa butter, 5-20% shea, and others vary as well. Here is one link with suggested amounts in soap: http://www.lovinsoap.com/oils-chart/
You can experiment as make single oil soaps and you will find they all make soap as well as what properties each oil might bring to the soap. Or just experiment on your own, because each person's skin is slightly different in what it likes and responds well to, like for some CO is not well tolerated. Some have allergies and sensitivities to certain oils. It really is a personal thing what one likes best in soap.
Soy wax is another good soap hardening oil to use. It is not like your traditional Waxes, and can be used at higher percentages than cocoa butter to produce a harder bar of soap that is not brittle. If interested, do a search on this forum for soywax and give the results a read. Here are a couple of links to get you started if interested:
. (Several posts in that thread delve into using soy wax in soap.)
(A few posts in this thread discuss using soy wax in soap.)
And here is a link on the subject of how to design the 'absolute best' soap formula (best is a relative term, though, so keep in mind people's skin vary as do our reasons for using or not using certain oils vary): https://www.modernsoapmaking.com/secret-to-the-best-soap-recipe/