for hair/reroot tools it is usually recommended you buy from
dollyhair.com, however lots of other sites sell the equipment too. dollyhair is good because its user-friendly and she carries pretty much every single hair color you could want, for about the same price as everywhere else. if you're using it for ponies, she sells pony-sized hanks
here.for paints, it is recommended that you use very watered down acrylics. any kind will do usually. you can find lots of acrylics and micheal's, joanns, walmart, hobby lobby, etc. Brushes aren't that important. you'll probably want a set of small brushes over big ones, so detailing is easier. (IE something like
this) lots of people think having like, sable hair brushes and whatever is important, but it's not really unless you're a professional painter. for a starting out kit, just a cheap brush pack from micheal's will be fine. you can always upgrade later.
the clay you are searching for, i'm assuming, is called apoxie sculpt. it's easily found on amazon, but i beleive you can also find it at hobby lobby, maybe micheal's but im not sure.
i recommend checking out
MLP Preservation Project for finer details on supplies, techniques, etc.