I can't answer your question regarding when the Varna began ("Caste" comes from the Portuguese "Casta"). And I'm not sure if historians are quite aware of where it came from other than the quotes from the Vedas regarding the Brahmins coming from Brahma's head, the Kshatriya coming from his arms, the Vaishya from his thigh, and the Shudra from his feet. This reference which there has been made much ado about has been quoted quite a bit, but there has been recent scholarship that questions its authenticity.

As for its clash with Buddhism, I can expound on that a little bit. It's often retold that the Buddha Shakyamuni (a Kshatriya) was against the Varna. This is not accurate. What made the Buddha and Buddhism different from the Vedic religion of the day, however, was that Buddhism held that Varna was not an impediment to enlightenment. The Vedic religion of the day held (mostly) that to be enlightened and achieve liberation, one must be (re)born a Brahmin.

As I've written about before, this may have been one of the contributing factors to the decline of Buddhism in the subcontinent. The common Indian was steeped in Varna and all its ceremony and tradition. The Buddhist monasteries, which were eschewing a lot of traditional ritual that was so important to the commoners' lives, seemed less and less relevant and turned more and more inwards. Though if we are to understand contemporary histories of Indian Buddhism, it's clear that the most cherished and well-known Pandits were from the upper classes, typically the Brahmin. Similar to the religious field in Europe, technically the Sangha was an egalitarian organization, but in practice, the high-born and well-connected dominated.

Anyway, Buddhism saw a grand revival in India in the modern period. The origin of this revival was B. R. Ambedkar, a well-educated "Untouchable." Fed up with being treated like his country's lowest members, Ambedkar converted to Buddhism and began a more socially-focused Buddhist movement in India, especially among the Varna-less Untouchables. While outside of India, Gandhi is well-known and his pacifism is quite loved, within India, Ambedkar is often the more venerated hero of pacifism, as it was he who sought to overturn the status-quo, while Gandhi didn't seem that bothered by the Varna system (though he did have a special affection for the Untouchables, trying to get the term "God's Children" to stick, while Ambedkar hated the term, saying it glorified poverty and oppression).

Without more specific questions, that's pretty much the connection between Buddhism and Varna.

Sources:

India: A History by John Keay

A Concise History of Buddhism by Andrew Skilton

Indian Buddhist Pandits trans. Tsonawa