Isaac's birth came about from a miracle - Abraham was 100 years old when Isaac was born (Genesis 21:5), and Sarah, at age 90, had been unable to have children (Genesis 16:1, 17:17). As explained, "Then God said, "Yes, but your wife Sarah will bear you a son, and you will call him Isaac. I will establish My Covenant with him as an everlasting covenant for his descendants after him." (Genesis 17:19).
Isaac was not Abraham's firstborn, or only, son. Fourteen years before, when Abraham was 86 (Genesis 16:16), Sarah (then called Sarai) had arranged for a child to be born to Abraham through her own Egyptian maidservant, Hagar. Ishmael was born from the arrangement (Genesis 16:1-4).
The promise did not go through Ishmael because the covenant had already been made with Abraham, with a yet-unborn Isaac the designated heir, before Ishmael was born (Genesis 15:2-6). While God does not play favorites, He was also not bound to any other arrangements for children that Abraham and Sarah had taken upon themselves to bring about after the matter had been firmly decided by God.
Nevertheless, God did see that Hagar and Ishmael would be greatly blessed - "I will so increase your descendants that they will be too numerous to count." (Genesis 16:10). The Arab nations of today, as they themselves will correctly tell you, are the descendants of Ishmael. Both the Jews and Arabs are descendants of Abraham. That is why they struggle, with often bloody and tragic results, over control of the Tomb of The Patriarchs in Hebron, in which Abraham is buried, right to this very day. Both, correctly claim descent from him - the Jews through Isaac, the Arabs through Ishmael.
Abraham's greatest test of obedience to God involved Isaac. "Then God said, "Take your son, your only son Isaac, whom you love, and go to the region of Moriah. Sacrifice him there as a burnt offering on one of the mountains I will tell you about." (Genesis 22:2). Abraham passed the test, while God stopped it before any actual harm to could come to Isaac - "Do not do anything to him. Now I know that you fear God, because you have not withheld from Me your son, your only son." (Genesis 22:12).
Abraham had been willing to give up his son to God, just as God Himself would later give up His Own Son to a sacrifice that was allowed to happen. An interesting point is that the place where Abraham was sent to sacrifice Isaac, Mount Moriah, is today known as the Temple Mount in Jerusalem - Isaac would have been sacrificed very near the place that Jesus Christ was Crucified.
At the age of 40, Isaac married Rebekah (Genesis 25:20). After they had been married for 20 years, they had twin sons, Jacob and Esau (Genesis 25:23-26). Jacob eventually became the sole heir of the promise - a very hungry Esau foolishly sold his birthright for a bowl of stew (Genesis 25:29-34), and Jacob obtained the blessing through deception of the then nearly blind Isaac (Genesis 27:1-40). It was while he was fleeing Esau's wrath for that deception that Jacob had his Stairway To Heaven dream.
Isaac lived a very long life before dying at Hebron. There, he was buried by Jacob and Esau in what is today known as the "Tomb of The Patriarchs" - the burial place of Abraham, Sarah, Isaac, Rebekah, Jacob/Israel and Leah. (Genesis 35:28-29, 49:31)
Fact Finder: What did Abraham believe that God would do if he had actually gone through with the sacrifice of Isaac?