I'm hoarding these fabrics like a dragon hoards gold.
Don't worry about sourcing supplies, though. With some links and some good practices, you can reliably source the best materials available, almost anywhere, thanks to the internet. And if I'm honest with you, it's a boon because nothing terrifies my social-anxietied heart more than interacting with hard-sell salespeople. Or just people in general. Moving on!
Tips for selecting fabrics online:
The best stores describe fiber content, weight, and hand. Look for places that allow you to zoom in analyze the weave and print. With practice you should be able to identify problems with weave irregularity, fiber content and weight fairly reliably by observation. Like anything it takes practice. Always be observant, analytical, and skeptical as you can when purchasing online. Like me you'll find yourself at a point where a disappointing purchase is rare indeed.
Below is a list of online fabric retailers I have used with success.
Fabric Mart : I love you Fabric Mart. So much. They have frequent sales, big bargain selections, coupons, affordable fabrics in great variety as well as well as high end fabrics and honest to goodness designer fabrics from Armani, Versace, and Anna Sui, just to name a few. They also have responsive customer service and fast affordable shipping. I personally have had a very good experience with them.
Dharma Trading : I've mentioned them before as it's where I get all my paints. You can get a large variety of undyed fabrics here including silk and linen, as well and any dye or fabric paint you could need. Good prices, top notch customer service. Just a fantastic company. Fast, environmentally friendly shipping to boot.
Vogue Fabrics : I always but my cotton batiste here. Hard to find stuff.
Fashion Fabrics Club : I like this place due to it's large inventory and I've stocked my studio with basics as well as special fabrics from here for many years. That said they have an older style inventory system and sometimes you'll get an email a week later saying your fabric since been sold out and isn't available to you. So, it can be a crapshoot. I can't speak for their customer service personally, but you can find the nitty gritty at Pattern Review.
Fabric.com : Frequent sales, but also suffers the infamous inventory crapshoot. But if you're lucky you can get some big bargains on basics here. Me, I use this for stocking up on basics when I have no pressing, immediate need. I find it useful. A lot of people have had very mixed experiences- check Pattern Review :)
I'm Stuffed Fur : Faux Fur; I use it often on coat collars. This place has a great swatch system and is really helpful. Their high end faux furs are so beautiful.
Those listed above are the sources I use the most, but of course there are a lot of places out there. Here are some other fabric stores I know of whose inventories impressed me but haven't personally used just yet:
Variety
http://www.moodfabrics.com/
http://www.gorgeousfabrics.com/shop/index.php
http://www.nyfashioncenterfabrics.com/
Custom prints (woohoo!)
http://www.spoonflower.com/welcome
Knits
http://spandexworld.com/
Silks
http://www.thaisilks.com/
http://www.printedsilkfabrics.com/
http://www.fabricandart.com/
Linen
http://www.mcssl.com/store/gray-lines-linen-inc
I will have whole separate posts dealing with sourcing antique and vintage kimono fabrics, so look out for that later.
And of course we need Notions:
B.Black and Sons : Traditional tailoring supplies, lots of specialty stuff.
Trim
http://www.mjtrim.com/
http://www.ejoyce.com/
http://www.moodfabrics.com/trims.html
http://www.voguefabricsstore.com/Bridal-and-Special-Occasion-Trims/
http://www.britexfabrics.com/lace-trim/beaded.html
Buttons and Bukles
http://www.ejoyce.com/pmain?cmd=e_sublist&depth=1&acode=0001&bcode=00010025
http://www.ascuteasabutton.com/?source=gppc&gclid=CMfz3PTtyowCFQ5cUAodqxKwYQ
http://www.patternsoftime.com/products.asp?cat=3
http://www.buckleguy.com/?utm_source=BG20131105&utm_medium=email&utm_campaign=BG20131105
http://www.buttonshoppe.com/000.htm
http://www.twinrosesdesigns.com/Buttons%20for%20Sale.html
You can also look at Etsy.com if you're in the mood for some vintage notions. When I do repro fashion, I go to Etsy for authentic antique notions.
I'll add to this list as I find more resources- happy hunting.