Who became the first leader of the muslim community after the death of muhammad?

Abu Bakr was the first caliph.

This choice was disputed by several companions of Muhammad, who believed that Muhammad had chosen Ali as his successor. It led to division of islam into Sunni and Shiite.

The Sunnis allege that Ali accepted the subsequent leadership of Abu Bakr, Omar and Uthman.

Primary sources are usually  more accurate and are written by someone who experienced it or witnessed it. secondary sources are those who heard of it after the fact that can lose details and or twist the event in a light that benefits them.