Little is known of his childhood, including his education and if he was infact intended to be a bishop. Its not even clear where he was raised. By the time he was 7 his second brother was dead. He received military training and was knighted at 18.
His English birth would help little. After William I died, he lived at his brother Robert's court in Normandy, losing his British lands to Rufus in anger over supporting Robert. Robert didn't trust him, imprisoned him and after Henry saved him from a siege, joined with Rufus and made war on him. It was when Henrry, who was popular and powerful in Western Normandy aligned with Rufus instead, he started going back to England.
He was smart though. He reverted back to many Anglo-Saxon laws, he removed oppression of the church his brother and father instilled. He also had an early bond with native Welsh princes (ended). Marrriage to Matilda made Scotland an ally. Robert invaded, he was eldest of all 3 brothers, and most Norman barons backed him. Henry had mainly Saxon barons, his brother in law's Scottish troops and the Welsh. His claim was based on old law (primogeniture not common yet) on an old law which stated since he was born when his parents reigned, unlike Robert who was borrn when they were duke/duchess, his claim was superior.
His best move was his marriage. Matilda not only brought her brothers' support, but she strengthened his claim Matilda was descended from the Anglo-Saxon kings of Wessex. Her mother was a granddaughter of Edmund Ironsides.