Probably the best source for Jewish ideas of the Messiah is the writings of the Essene sect, found in the Dead Sea Scrolls. The Essenes seemed to have two separate Messiah figures/ideas–a suffering servant and a conquering king. They tended to focus on the priestly nature of the Messiah. This may reflect their rejection of the priesthood in Jerusalem as corrupt.
The New Testament, of course, reveals the Jewish messianic expectation that the apostles, and, presumably the biggest number of common Jews had, which is for a conquering Son of David. Like Peter said, "Are you now going to restore the kingdom" (Acts 1:6). Here, even at the end, the apostles were still expecting Jesus to restore political power to the Jews. Clearly, Judas expected Jesus to be a conquering king. He hoped to manipulate Jesus into rebelling against Rome when he had him arrested. There were a number of Jewish expectations of the Messiah, as there are different interpretations of the actual Messiah, Jesus, today! I am no expert, and you may want to do some of your own research, but the way I undertand it the most common Jewish expectation for the Messiah was as a "Son of David", to come as a conquering Messiah, restoring the political fortunes of the Jews. Ezekiel 37:24-25 is one of many messianic passages which calls the Messiah the Son of David. It should not be surprising to us that the Jews had this expectation. Many OT passages clearly depict a victorious Son of David. The problem is that these Jews failed to notice the Messianic prophecies which presented a Messiah not to their liking. The Essenes did have a concept of a suffering servant (Isaiah 53), but it seems that the Jews, in general, did not tend to pay nearly as much attention to this role of the Messiah. This should not surprise us, as this is human nature. Humans want their heroes to conquer and to offer great things to the people, not to suffer and die.
Jesus, of course, as the Messiah, is suffering servant, prophet, priest and king. Passages in the Old Testament revealing all of these natures for the Messiah can be shown. In one place or another, the Jews had all of these expectations, depending on which messianic prophecy they focused in on, and, of course, on their own personal prejudices.
It is not hard to see, and I am sure you already noticed it, that as the Jews treated their Messiah, so Christians treat Jesus today. Many make him into a cosmic bellhop–delivering blessings and solving all problems. Theirs is the Jesus of name-it-and-claim-it: the prosperity gospel. Others who have strong convictions about social justice make a Jesus to their liking. Still others, premillenialists, have him coming back to be the head of a revived Jewish Kingdom at the end of time. The lesson for us is that we, too, are tempted to form the Messiah in our own image. Let us see clearly Jesus in a balanced, biblical way.