Note: I am not sponsored by any of the products I list here I just want to help others if they also wish to make fursuits and don't know where to buy certain things. I live in the USA and thus all these store/brands are things I have purchased within the USA.
Sewing Machine:
Brother CS5055PRW
Faux Fur:
BigZFabric / Howl Fabric
Minky:
Missouri Star / Etsy / Howl Fabric / BigZFabric
Lycra / Spandex (Lining):
Joann
Upholstery Foam:
Michaels / Joann
Craft Foam (Eyes):
Michaels
Crinoline (Eyes):
Joann
Felt:
Michaels
Yarn (Fur wefts):
Michaels
Thread:
Joanns / Missouri Star / Michaels
PVC Vinyl (Paw Pads):
Fabric Wholesale Direct / Joann
Polyfil:
Michaels / Joann
Acrylic Paints:
Michaels
Vinyl Floor Runner (Feet Soles):
Lowes
Zippers:
Joann
Magnets:
Michaels / BuyMagnets
Elastic:
Joann
Bias Tape:
Joann
Laminator And Sleeves:
Michaels / Office Max / Walmart
Badge ID Clips:
SpecialistID
Gluesticks:
Michaels / Joann
E6000 Glue/ Shoe Goo:
Michaels
Andis Easy Clip Whisper:
PetsMart
Contact Cement:
Walmart
Squeakers:
PetSmart
Full Body Coveralls (Duct Tape Dummy):
Lowes / Home Depot
