Ahmed Rashid and Peter Bergen have both written multiple books that answer this question in depth.

In short and very simplistic, Pakistan has always been very focused on India as their main adversary. In order to not have problems on both its borders, Pakistan had adopted a strategic-depth policy for Afghanistan. If Afghanistan, or at least the border with Afghanistan was ruled by Pashtun factions, it would be less cause for worry than if the Turkic or Hazara peoples in Afghanistan would be the main players, as this would increase the influence of the bordering Central Asian states and Iran. In Pakistan, there was also the idea that these groups would be more sympathetic towards Indian interests in Afghanistan than a Pashtun-dominated Afghanistan. An Afghan communist regime allied to the Soviet Union also really was not in Pakistan's interests.

In order to achieve this, Pakistan started to mainly support Pashtun groups that fought against the Soviets and the Afghan communist government. A lot of the support from the US was distributed by the Pakistani ISI to the Pashtun faction led by Gulbuddin Hekmatyar. This group received the bulk of material and logistical support.

When the Soviets withdrew, the US was not involved much anymore, and Pakistani support was maintained for the Pashtun factions in their fight against the communist Afghan regime. When this regime fell, the civil war continued between the Pashtun forces, and the Tajik, Uzbek and Hazaras in at times differing alliances.

The Pashtun forces of Hekmatyar had however received such a bad reputation, even among the Pashtun population, that when the Taliban emerged as a grassroots organization within Afghanistan, the Pakistanis started supporting them as a better option to take care of their interests. With Hekmatyar besieging Kabul, and Pakistani material support and support of the Pahtun locals shifting to the Taliban, it did not take long for the Taliban to overrun Hekmatyar from the south and advance into the territories of the other warlords.

So then the Taliban controlled most of Afghanistan. Hekmatyar had fled to Iran. The remaining Uzbek, Tajik and Hazara warlords created the Northern Alliance. They held on to a small area in the north of Afghanistan and received limited support from the Central Asian states, Iran, Russia and India. All these states did not want a Taliban-regime on dominate the whole of Afghanistan, but they did not give enough support to defeat the Taliban. There was the idea that the Taliban and their allies could go on a campaign throughout Central Asia.

Also of importance, the Taliban had genuine grassroots support from the Pashtuns and many saw them as the only way to finally stop the civil war, making them a good pick for Pakistan. However you may think of Islamic fundamentalism, it is a simple and effective form of governance.

The problems with the Taliban and the Pakistan-US relations only came up after the Al Qaeda embassy bombings in Kenya and Tanzania, and of course 9/11. But before that, the US did not really care about Pakistan's support for the Taliban, just like the US was basically not involved in Afghanistan since the Soviet withdrawal.