A Basic summary of the expectations which Jesus fulfilled.They expected him to free them from the Romans and bring in a great time of world peace and a holy nation. But they alsohad many other expectations which are in differing degrees, not necessarily those recognized by Jews today.
Prophesy in Zacheriah shows that the name of the Messiah would be the same as the name of the high preist in Zerubabel's time (the name was Joshua)! Also sorts out the origin of the two Messiah theory and shows that they are really the same Messiah.
Skeptics often point out that Messianich predictions such as Ps 22 are "bad translations from Hebrew. These can be explained as they are translations from the LXX (The Septuagent--the Greek Translation of the OT made in Alexandria by Rabbis in the Intertestamental period). Sketpics continue to argue that the LXX is invalid but they are wrong. The LXX was the Bible of the Early chruch and it was a valid textual choice among many Jewish groups such as the Apocryphal writters and the sect at Qurman.
A close and extended study of the dialogeical pattern in Isaiah shows that the Suffering Servant of chapter 53 has to be the Messiah. Not only is it his turn in the pattern to be the object of foucss, but if the pattern was disrupted it woudl disrupt the roles played by Servant and Israel and undermine the message of the whole book.
Rabbis throughout the ages, even before Jesus' time, affirmed that the Suffering Servant of Is 53 is the Messiah. To the extent that Jesus fits the description of the Suffering Servant, he must be Messiah.
Skeptics use the curse of Jehoacin (last King of Judah) in Jeremiah to argue that the curse on that line was never lifted. Jehoachin is part of the geneology in Matthew, doesn't invalidate Jesus as Messiah?
Some Skeptics argue that since one could inherit the throne only from the father's side, and since Jesus was not blood kin to Joseph he would not be eligible to inherit the thorne, thus cannot be Messiah.