Okay, I'll take a stab at this...
1. M&P is not soap 'making', so much as soap 'assembling'. You're just taking a pre-made soap base and adding stuff -- colors, scents, additives.
2. Since you are doing M&P, I'm not sure why you are asking about preferred oils ... but here goes...
Oils are composed of fatty acids, right? There are 8 that are most commonly seen in soaping. These 8 acids will contribute different things to a bar of soap. Coconut oil mostly contributes drying/stripping and bubbles. Therefore, most people will not be happy with a coconut-heavy bar and especially not with a 100% coconut oil bar. Suggested maximum usage is 30% for coconut, but in practice I prefer a max of 10 - 20% because my skin is ... ahem ... old, and not as oily as it used to be.
A Soap Making Oil Chart, followed by Fatty Acid Profiles, and Fatty Acid Properties can be found here:
http://www.lovinsoap.com/oils-chart/
Right off you see Coconut, and the suggestion to 'superfat' a 100% CO bar at 20%. Two things about this approach: It doesn't work particularly well, and is a waste of money since those superfatting oils are going down the drain faster than the saponified ones. (P.S., if you are not familiar with these terms and concepts, you have a lot more reading to do.)
I suggest getting very familiar with the oils listed -- there are a lot of great tips and comments at that link -- and figure out first what you want the soap to be like, based on what soap is capable of being. (E.G., it is not capable of being lotion.) Then peruse the oils for which ones will deliver your preferred results. Hint: most oils have at least one substitution, castor being the exception off the top of my head, so once you know what you want you can choose based on price, availability, or any other qualitative/quantitative measure you desire.
Hope this helps. Happy soaping!