How are the major ablution (ghusl) and the minor ablution (wudu) performed as reported from the Prophet ﷺ, and with the differences among the schools of thought, whom should I follow?

It is not obligatory to follow a specific madhhab; rather, one should ask trustworthy scholars and act upon what they clarify. As for the major ablution (ghusl) from major ritual impurity (hadath akbar), it has two forms:

An adequate form, which consists of the intention, then drenching the entire body with water once, along with running fingers through the hair, rinsing the mouth, and sniffing water into the nose.

A complete and recommended form, which is: the intention, saying "Bismillah" (in the name of Allah), washing the hands three times, washing the private parts, performing wudu' as for prayer, then pouring water over the head three times and running fingers through the hair, then drenching the entire body with water, starting with the right side then the left.

Ghusl from major ritual impurity is sufficient for wudu', unless any of the purity-invalidating factors occur.