Vendors for US (I see you are in NY)
For Micas, most often I use
Nurture Soap (in Indiana) &
Micas & More (in Kentucky). I also have
some from Mad Micas (in Florida). All are very nice. There are so many vendors out there that really get good reviews from our members, but I have not tried them all. Rustic Escentuals in South Carolina sells micas, but I have only used samples I picked up along the way at soapmaking conferences, so can't give a lot of feedback on their micas.
If shipping costs are a concern, as they are for so many of us, look for vendors closer to home, but pay close attention to the descriptions (particularly if the mica in question is for cold process soap, as some micas are not lye stable), and even better if they show what the color looks like in CP soap.
For FOs, there's a really useful spreadsheet here at SMF that lists reviews by SMF members on tons of FOs from all kinds of different vendors, It's a great resource. See this post and scroll to last page for more recent information about the upkeep of the spreadsheet. You can always find the link to the spreadsheet in that thread & also in DeeAnna's signature at the bottom of any of her posts, like this post, for example.
But, feel free to ask for specific advice on FO's or EO's here in Shopping Recommendations as there are so many members here with tons of experience with fragrances that can steer you in directions to obtain well tested fragrances. Always pay close attention to the reveiws & descriptions of how a fragrance behaves in soap and also safe usage rates for soap. These are very important considerations for fragrances.
For oils, my vendor of choice is Soapers Choice (in Illinois), although I do occasionally buy elsewhere when the price is right. They are very near me geographically, so shipping is low for me; not sure how being in NY would add up when it comes to shipping costs. Some folks on the East Coast like Jewards International (in MA). Generally I buy Coconut Oil and Olive Oils only in grocery stores or grocery outlet stores because I get better prices that way. If you want to use lard, try Walmart. For tallow you'll probably have to use an online supplier or render your own.
For Lye, I prefer Essential Depot (in Florida) when they have sales (otherwise it's rather expensive), but on sale, it's pretty darn bargain basement for me. Plus I like the bottles their lye comes in, because of the great air-tight hard-to-open child-proof (almost adult-proof it's so good) cap. AND these bottles are perfect for me to keep my master-batch lye solution in after I make it. They are already labeled for me and they are very sturdy & do not deteriorate with lye solution (HDPE plastic). There are plenty of other vendors, many here like The Lye Guy (in NY). His prices are really good, especially if you can pick it up yourself in Pennellville, NY. I actually had some NaOH from The Lye Guy and it was certainly fine lye, but I don't like the flimsy bottles at all. But for a New Yorker, I think it's probably the best price you'll find.