Who was Israel's favorite son?

Answer 1

Joseph.

This raises the question: did Jacob (Israel) show favoritism?

According to Jewish tradition, Jacob showed encouragement towards Joseph; not what we should call favoritism. All of Jacob's young sons were striving for righteousness (and Jacob never suspected that dangerous jealousy might arise). Among pious scholars, "jealousy breeds greater scholarship" (Talmud, Bava Batra 21a), because they direct the instinct for jealousy only towards the outlet of positive competition. Jacob saw that Joseph was, at the outset, the wisest of his sons (Targum, Genesis 37:3) who had absorbed all of his (Jacob's) teachings (Rashi commentary, ibid) at a young age. Also, when Joseph saw that his half-brothers born of Leah were more friendly among themselves than with their half-brothers born of Bilhah and Zilpah, he took the initiative to open up to the sons of Bilhah and Zilpah (Midrash Tanchuma, Vayeshev ch.7); and he also spoke with criticism concerning the sons of Leah (Genesis 37:2; Rashi ibid) in order to spur them to improve the ties among the bothers.

Because Jacob observed Joseph taking the most initiative in wisdom and righteousness, he took action, giving him the gift of a special coat (Genesis 37:3) as a token of leadership, to provoke the positive kind of "jealousy among scholars." Even after the unfortunate result (Genesis ch.37), Jacob never rescinded the gift or regretted it, since he himself had not erred in judgment (it was only the bothers who erred, as they later acknowledged [Genesis 42:22]); and he even reiterated Joseph's high status decades later (Genesis ch.48-9).

Answer 2

The predominant person after Joseph's death is Ephraim - called the firstborn by God. He is referred to as the head and he and his brother Manasseh are the 'birthright' holders. There are many Scriptures mentioning this, here is one:

Psalm 60:7New King James Version (NKJV)

7 Gilead is Mine, and Manasseh is Mine;

Ephraim also is the helmet for My head;

Judah is My lawgiver.