What might surprise many Christians is that the Jewish messianic concept developed largely after the time of the Maccabean Revolt (167 BCE) that led to the first celebration of Hanukkah. This occurred after the books of the Prophets were largely completed.
Many Christians do not realize that after the success of the Jews over their Seleucid counterparts, the Jews once again had a line of Jewish kings ruiling over them and thus freedom from Gentile influence. This, oddly enough, is what may have led to the messianic concept...and this is why.
The line of Jewish kings of that specific era were in the line of Judas Maccabeus, and even though they had won a great victory for their Temple and Jewish worship, corruption soon set in. The Hellenism that the Maccabees fought against was soon adopted by their rulers, and they also made a marriage pact with an odd family that had ties with a small and seemingly insignificant country at the time--Rome. The family? The Herods.
You probably know the rest of the story and what happened next.
The Jews blamed the problems that came next on the fact that Judas Maccabeus was of the tribe of Levi. The Jewish Law states that rulership is to come from Judah. As Rome grew, and the Heords devoured the line they married into and took over the rulership of the Jews, the priesthood and scribes, studying the Law and the Prophets, noted that the anointed one was promised to rise from the house of David. Thus an expectation for a future "anointed" one came about.
"Anointed" in Hebrew is of course where you get the English word "messiah."
While there are no direct prophecies in the Hebrew texts that talk about the Jewish messiah (including the above from Isaiah 49), the Jews did start to hope for a future monarch that would restore the Kingdom of Israel and overthrow both the Herods and release them from Gentile intererence. But the Jews did not believe in a "suffering" messiah. Where did that come about?
When Jesus of Nazareth was arrested and subsequently crucified by the Romans, the Christians would later apply the Suffering Servant Songs of Isaiah (which are personifying Israel as a slave suffering at the hands of Babylon during the Exile) to what Jesus went through and claim it was a forecast of events to what he went through on Good Friday. These Songs have been traditionally sung as a series of haftorahs in synagogue services as lessons mouring the events of Jewish persecution--not only the Exile, but today they are now also used by the Jews to mark the Spanish Inquistion, the pogroms, the Crusades, and the Holocaust.