I am trying to understand the evolving Catholic doctrine on this. One of its strengths is the priesthood. Isn’t the purpose of Apostolic Succession keeping the authority to act in God’s name? Isn’t the priesthood essential to that?
So which of the Seven Sacraments can lay people perform given the correct intent, matter and form?
What is your interest? What faith community do you belong to?
Narses has given you the correct answers, or pointed you where you can find them.
Baptism CAN be performed by an lay person with correct intent, matter and form. Normally that would only be done if there is some good reason to do so--otherwise, it would be done in church by a priest with sponsors.
Also, the Catholic Church keeps records of baptism, so it should be reported to the baptized person's parish church (possibly chosen after baptism) and entered into the records. And the priest might decide to do a conditional baptism in addition, to be sure that everything was valid.
Marriage is the other sacrament that can be performed by lay persons. In fact, the bride and groom administer the sacrament to each other with the ring and the words, and the priest is said to preside over the sacrament. Non-Catholics also can validly marry, but not sacramentally. Catholics normally should marry in church at Mass, presided over by a priest, and properly witnessed, but as with baptism can marry one another privately if there is a sufficient reason or emergency, and then have it confirmed or preferably performed again in church with a priest and witnesses. At least, that is my understanding.