I used BB as my main supplier, but have also recently used The Scent Works for FOs and Essential Depot for lye.
As to shea butter....I've been buying it for about 5 years or so to use for my daughter (who has eczema). I tried a lot of different places, but have consistently found the best quality and prices by far is Coastal Scents. Especially if you are able to catch them when they have a sale (I've gotten bulk unrefined shea for $3 and $4 per pound, free shipping).
Personally, I've only purchased the unrefined as I have mainly used it for topical application (direct skin benefit) and I feel it retains it's natural qualities/benefits better before it's refined. If I'm going to put it on the skin, I want the full benefit of it! When I started using it in soap, I just used the shea I had on hand since it was such a great price. You can google refined vs. unrefined shea and read LOTS
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I tried ordering Shea (unrefined) from Columbus Foods (Soaper's Choice) with my last order and was super disappointed. I paid the shipping to return it as it was just that bad to me. Appearantly, I might be one of the only people who have had problems with it, but it just didn't meet my standards.