I am a yoga instructor. I teach a physical, mental and spiritual practice that originates from India.
How interesting! What is the most challenging form of yoga?
There are so many varieties of yoga from originating from Hinduism, Buddhism and Jainism. I would have to say that a type called Ashtanga Yoga is the hardest. 
That does sound pretty tough. What kind of equipment do I need to start yoga?
For beginning I would try Hatha or Raja yoga. But you just need a mat. It can help if you have a belt and a block as well. 
I think I have those lying around the house somewhere. How long has Hatha been around for?
The origins are a little vague. But it's believed that it dates to pre-vedic times around the 5th or 6th century BCE.