Which two posts were held by Sardar Patel during the crucial period immediately following Independence?

Deputy Prime Minister and Home Minister.

Sardar Vallabhbhai Patel (1875-1950):

He was a leader of the freedom movement & a Congress leader from Gujarat.
He was a follower of Mahatma Gandhi and participated in various movements with him.
He was the Deputy Prime Minister and first Home Minister of independent India.
Also, he was a member of important committees of the Constituent Assembly on Fundamental Rights, Minorities, Provincial Constitution, etc.
He played an important role in the integration of Princely States with India.