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?
to pre-Vedic Indian traditions; it is mentioned in the Rigveda, but most likely developed around the sixth and fifth centuries BCE, in ancient India's ascetic and śramaṇa movements. The chronology of earliest texts describing yoga-practices is unclear, varyingly credited to Upanishads. The "Yoga Sutras of Patanjali" date from the first half of the 1st millennium CE, but only gained prominence in the West in the 20th century. Hatha yoga texts emerged sometimes between the 9th and 11th century with origins in tantra.
Yoga
Yoga
Yoga (; ; ) is a group of physical, mental, and spiritual practices or disciplines which originated in ancient India. Yoga is one of the six orthodox schools of Hindu philosophical traditions. There is a broad variety of yoga schools, practices, and goals in Hinduism, Buddhism, and Jainism. The term "yoga" in the Western world often denotes a modern form of Hatha yoga, yoga as exercise, consisting largely of the postures called asanas.
The origins of yoga have been speculated to date back