The answers to your questions would be enough to fill several disertations, but here's my attempt to be short and concise.
There are two main branches of Islam - sunni and shia. The differences between the two can be boiled down to authority. Who has the authority to suceed the Prophet (saws)? Who has the authority to rule? Who has the authority to make religious law?
Sunnis are those who believed that the authority to suceed the Prophet (saws) laid in the hands of his closest companions, and it was for them to chose who would rule. Shia are those who believed that the authority to suceed the Prophet (saws) lay only with his family.
From there, two religious traditions emerged. Throughout history, they've cross pollinated, with great scholars in each group studying with scholars of the other group. But in the end, we both turn to those with authority within our own groups.
Among sunni muslims, authority lies in the Qur'an, the sunnah (traditions of the Prophet as collected by sunni scholars) and in the ijma, consensus of scholars of sunni islam. I am not familiar with shia thought much beyond the basics, but for them, authority again is drawn from the family of the Prophet (saws) through the imamate, the descendants of the Prophet (saws) who were the religious leaders of the shia community. I believe that for them, their sources are the Qur'an, and the Sunnah as interpreted by the imams.
Kharajites are an early sect of muslims that had issues with authority (ah see, it all comes back to authority). They were originally shiat Ali, partisans of Ali, believing that God had appointed him as the Imam of the muslims. However, when he acted in a way that seemed to contradicted how the annointed of God should act, they killed him.
Sufis are not a seperate group. They are either sunni or shia muslims who practice the religious science of tasawwuf, the inner science of self, of purification of the heart. There are "goofy sufis" who have seperated themselves from Islam and gone universalist, but they can't really be considered as muslims and as such, aren't really a branch on the tree of Islam.
Myself, I'm a muslim of the sunni variety, following the school of jurisprudence of Imam Shafi'i, and beginning to tread the path of tasawwuf in the order of Abul Hassan ash Shadhili, God willing.