Why Christianity and not Judaism?

Christianity is the fulfillment of the promises and prophecies of Judaism.  Jesus Christ is the Messiah of Judaism.

Read about an account of the crucifixion of Jesus that was written at least 2 centuries before he walked the earth.  This is a part of the Jewish scriptures:
"But he was wounded for our transgressions;
   he was crushed for our iniquities;
upon him was the chastisement that brought us peace,
    and with his stripes we are healed."

Read the entire passage here

Why the God of the Bible?

One god is simpler than many.  That leaves Christianity, Judaism, and Islam as the only major world religions of one God (mono-theism).

Judaism and Christianity both start at the Bible which makes that a book worth checking out (even Islam allows for a bit of the Bible).  Judaism believes the Old Testament up to the time of Jesus and Christianity believes both the Old Testament and the New Testament.

The Koran of Islam came on the scene pretty late (7th century) and does not compare well with the Bible.  Muhammad, the prophet of Islam who brought the Koran, is also a bit of a disreputable character.