I am fairly new to the whole soapmaking thing, but this is my take on it. I personally prefer not to use crisco, but do use things like lard and soy. IMO at least lard and soy are natural oils, and not a manmade concoction. I know several people who learned to make soap using crisco and had a good soap that was affordable. I would look at what you want your budget to be as some of these oils can get really pricey.
You can make it as simple or complicated as you want. I would suggest finding a friend who has done it a few times as it really helps. For me... I can read about trace and about how to stir, but until I see it done it doesnt always click for me.
I personally like the addition of herbs via infused oils and adding in many different oils.
You can use the lye calculator at majestic mountain and come up with any combo that you like.
The mullerfarm website has some good info along with the miller site that has been previously mentioned.
These are the recipes that I made last week. I had made the cocoa butter soap before and it is great for kids... It is very rich and soothing, has a nice lather, and doesn't leave the sticky film that I often feel with some soaps. I infused the olive oil with lavender, lemon grass, and calendula and then scented it with lemon eo and lavender eo, but you could use anything. I had used cassia(cinnamon) the last time I did this one as I thought it went nice with the cocoabutter smell.
The peppermint recipe was a new one, and it isn't as white as I wanted, but I infused the coconut oil with peppermint prior to making the soap.
20 coconut oil(I'll infuse this with some peppermint)
20 soy oil
10 sweet almond oil
15 olive oil(I'll infuse with lavender and lemon grass)
15 coconut oil
9 cocoa butter
15 grapeseed oil