Ditto what Susie and Shari said.
Your quest is one that we are actually all on, but there are so many variables to take into consideration when it comes to formulating, such as individual skin-type, allergies, water-type, etc..., not to mention the fact that 'hardness' is a very subjective thing from person to person. More specifics would be very helpful in helping us to help you.
For what it's worth, though, the top 3 fats that contribute hardness to soap are as follows:
Tallow
Palm
Lard
Others that contribute to hardness (but are more expensive than the above 3) are butters such as cocoa butter, kokum butter, mango butter, illipe butter, etc...
Also, one of the surprising biggies that contribute to hardness is olive oil, but not as immediately as the above 3- it does so over time, eventually.
Coconut oil and palm kernel oil (PKO) also contribute much to hardness, but since they are also very high on the cleansing scale, you'll want to use them with discretion so that your soap doesn't end up too drying. Those 2 also happen to be 'bubbly oils' (they create much bubbly lather).
But hardness isn't all you should think about. A well-balanced soap should also have some conditioning oils in it, as well as lathering oils.
The best advice I like to give those new the craft is to 'start somewhere' by making a small batch of soap with a trusted recipe (such as the one Dixie posted, for example), cure it for 6 weeks, test it out, and then tweak things from there. For example, if it was too drying for you, then you can lower the cleansing oils next time or increase the superfat some, etc...
There is much advice we can give you to help you tailor your soap to your liking as far as your skin-needs or likes/dislikes are, but it's much easier to do so when there is a finished soap to use as a plumb-line.
IrishLass