Patterns of Fashion: The School for Historical Dress publishes these and other costuming resources, runs workshops, and administers the Janet Arnold Archive.
Burnley & Trowbridge - their focus is post-period, but they do have linen, silk, and wool, as well as notions & findings.
Daytona Trimmings - The most reasonably priced trim shop left in the Garment Center in NYC. They won't have everything you want, but you can afford what you need.
Fabric Warehouse - In Rahway, the best place to get brocades, velvets and silks in northern NJ, and they have great and frequent sales.
Gray Lines Linen Inc. - The best store in NYC for various qualities of linen, and where we did the group order.
Hai Trim & Feathers - Amazing NYC trimmings shop that will delight your inner drag queen and has great feathers selection.
Manhattan Wardrobe Supply - Theatrical supply house in NYC that has notions and cleaning supplies, spring steel and spiral corset boning selections, and all kinds of cosplay paints and dye supplies.
Mood - The most comprehensive fabric store in NYC. They have beautiful quality fabrics, buttons, ribbons, and some trim, of every sort, but they charge top dollar for them.
Pacific Trimming - Brand new trims and notions store on 38th Street, NYC. Huge range of options, but probably pricier than older places.
Sartor - a Czech-based fabric seller that has been making reproductions of historical brocades for many years (though most of their focus is pre-16th century). Their linen is also excellent.
SiL Thread - Comprehensive NYC notions and tools supplier, with garment bags and limited sizes in spring steel boning as well.
Steinlauf & Stoller - Old school notions and interfacings place in the Garment Center, NYC. Good for thread, zippers, interfacings and shears, needles and etc.
Tied to History - Mostly goldwork and spangles, but they carry a very fine linen voile is excellent for partlets, ruffs, or a high class chemise/shirt.
Tudor Tailor - Great online shop with materials, laces and their publications. Items ship from Nottingham, UK.
Woolsome - Polish-based fabric seller, specializing in wool (as the name implies), also carries linen.
Armour & Castings - Well known for their reproductions of period jewelry and leather fittings.
Fire Mountain Gems - semi-precious and other stones, as well as a vast array of findings and mountings.
Jamming Gems - Jewelry company that sells lab-grown gemstones and various fittings
Rio Grande - Jewelry supply company in NM, specializing in findings.
Sapphire & Sage - Ohio company that makes reproductions of 16th century jewelry and accessories
Tudor Jewels - UK company that reproduces jewelry from Tudor portraits.
Two Baronesses/Avalon Natural - SCA sellers based in GA, selling reproduction 16th-century buttons and various Viking accessories.
Higgins Creek - This company makes a wide variety of masks for parties, theatre, and LARPing.
Pirate Masks Studio - This Canadian company makes medieval and Commedia del'Arte themed masks.
Tiger Torre Art - leather masks of all kinds, including Carnival-themed.
Shoes
There are lots of places that sell a simple latchet or maryjane type of flat shoe that is a good approximation of Renaissance footwear. But these places specialize in period reproduction shoes:
American Duchess - America's best known producer of period shoe styles, including 19th and 20th century styles for tango and swing dancing, but expensive.
Armstreet - European company that makes nearly every part of a medieval, Renaissance, or fantasy kit.
Boots by Bohemond - Historic shoemaker in New Mexico, sells at Pennsic. Luke recommends the Saint Kathryn Slashed Shoe from Bohemond. These are very good for earlier in the period but can really work for the full period of 1550-99.
Collectibles Arena - On Etsy, they have a plain latchet shoe that seems to be pretty well rated. It has a low heel.
Graziano Dal Barco - This high end company makes bespoke, very high end, historically correct shoes in Italy. Best for our purposes are styles S49, S116, and S59.
Medieval Collectibles - Mail-order company in Indiana that specializes in fantasy and medieval clothing for LARPing and gaming. They have a plain shoe that is ok looking, the Katelyn Women's Medieval Shoe. They carry up to Euro size 44, which is a woman's 13 and a man's 10.5.
American Duchess: The shoemaker offers reasonably priced cotton and silk stockings.
Hero's Haven: Shipping time on these can be lengthy, so plan ahead when ordering.