I think just the survival of Christianity after Jesus' death, combined with the claim Peter, James, and the other apostles made to having seen Jesus alive after his death is pretty good evidence of the resurrection. The reason is because the whole movement centered around the notion that Jesus was the messiah. If you look at all the unambiguous messianic prophecies about the messiah, you see that his coming is always associated with the reunion of Judah and Israel, a full return from exile, the defeat and overthrow of all of Israel's enemies and occupiers (which would include the Romans), national sovereignty, the restoration of the Davidic dynasty, and the beginning of an permanent era of peace and prosperity that eventually extends to all of the nations.
So it was built in to the whole concept of the messiah that his coming would be a big triumph for the Jewish people, and there'd be no more occupation. For Jews living in the first century, that would mean no more Romans. They would live in peace and enjoy national sovereignty. These expectations are even reflected in the gospels. At one point the apostles ask Jesus, "Are you going to redeem Israel now?" At another point, a crowd tried to make Jesus king by force.
With all of these expectations in mind, the last thing you'd expect if you thought Jesus was the messiah was for him to be defeated and put to death by the very people he was supposed to have prevailed against. His death should have proved to any Jew in the first century that he was not the messiah after all.
And that seems to be the case. In Luke, there's a story about a couple of disciples of Jesus walking to Emmaus after Jesus' death, and one of them said, "We thought he was going to redeem Israel." They were disillusioned initially.
Paul said that "Christ crucified" was a stumbling block to Jews, and for good reason. There were several people in the first century who claimed to be the messiah. In each case, they'd gather followers and eventually be killed. Once they were killed, their movement ended. The followers would either find another messiah to follow or else do something else with their lives. During the first Jewish war with Rome, there were three people all claiming to be the messiah who were holed up in Jerusalem during the siege, fighting each other at the same time they were fighting the Romans. But nobody continued to believe in them once they were killed.
In the second century (around 135, I think), the Jews fought a second war against Rome, and practically the whole nation rallied around Simon bar Kosiba who they thought was the messiah. But once he was killed, not a single person continued to believe he was the messiah. His death proved he wasn't.
So there has to be some explanation for why Jesus' movement survived his death, especially since it survived his death as a messianic movement. Why did anybody continue to believe he was the messiah after he had been utterly defeated without having fulfilled all the major messianic prophecies? Keep in mind all of his earliest followers were throughly Jewish.
Well, the explanation they gave themselves was that they saw him alive after his death. There are a lot of scholars (probably a significant majority) who think they saw something they took to be the risen Jesus. There are some, like Gerd Ludemann, who think they had grief hallucinations. There are others, like E.P. Sanders, who just throw up their hands and say they don't know what they saw, only that it was what gave them confidence in Jesus.
I don't think a hallucination is an adequate explanation, though. Grief hallucinations are fairly common after a loved one dies. I had a really lucid dream about my dad after he died. My grandmother said she had an experience of my grandfather after he died. But these experiences never lead people to believe their loved one is raised from the dead.
Try to imagine what you would do if somebody you knew to be dead was standing in front of you right now. Imagine it's some close relative of yours who died. What do you think you would make of that? Well, you'd have multiple options. You might think you were dreaming, hallucinating, seeing a ghost, or that the person hadn't died after all. But probably the very last thing you'd think was that they had risen from the dead.
In one of the gospels, the initial reaction upon seeing Jesus was that they thought they were seeing a ghost. It wasn't until Jesus ate in front of them, and they could touch him, that they believed he was a flesh and blood human being. And there's lots of stuff in the New Testament about them actually touching the risen Jesus.
That makes a lot of sense if you think about it because probably nobody would've thought Jesus had risen from the dead just because they hallucinated him. It would've taken much more than that. So these reports about Jesus eating and them touching Jesus are probably true because nothing short of that really explains why they believed he had risen from the dead.
So, if Jesus really did die on the cross, and the disciples later were able to eat with and touch a living Jesus, then that's pretty good reason to think Jesus had risen from the dead.
That's the skinny of the argument, though. A whole book could be written on this subject.