The disciples risked their necks
That the disciples suffered is multiply attested. We have the martyrdom of Stephen recorded in Acts 7. We have the martyrdom of James the brother of John in Acts 12. Paul's sufferings are recorded in his own letters to the churches, most notably 2 Corinthians 11:
"Five times I received the forty lashes minus one from the Jews. Three times I was beaten with rods. Once I received a stoning. Three times I was shipwrecked. I have spent a night and a day in the open sea. On frequent journeys, I faced dangers from rivers, dangers from robbers, dangers from my own people, dangers from Gentiles, dangers in the city, dangers in the wilderness, dangers at sea, and dangers among false brothers; toil and hardship, many sleepless nights, hunger and thirst, often without food, cold, and without clothing."
We already mentioned the Jewish historian Jesus records the death of Jesus's brother James. (Antiquities 2:200) The martyrdom of James is also recorded by Hegesippus, a Christian chronicler of the 2nd century.
The witness of the early church fathers
Clement of Rome, a Christian pastor who was a contemporary of the apostles reports the sufferings and deaths of Peter and Paul. He wrote in 95 AD "Peter, through unrighteous envy, endured not one or two, but numerous labors; and when he had at length suffered martyrdom, departed to the place of glory due to him. Owing to envy, Paul also obtained the reward of patient endurance, after being seven times thrown into captivity, compelled to flee, and stoned. After preaching both in the east and west, he gained the illustrious reputation due to his faith, having taught righteousness to the whole world, and come to the extreme limit of the west, and suffered martyrdom under the prefects. Thus was he removed from the world, and went into the holy place, having proved himself a striking example of patience." (1 Clement 5:3-7)
Polycarp, another contemporary of the disciples also wrote of the disciples' sufferings: "I exhort you all, therefore, to yield obedience to the word of righteousness, and to exercise all patience, such as you have seen [set] before your eyes, not only in the case of the blessed Ignatius, and Zosimus, and Rufus, but also in others among yourselves, and in Paul himself, and the rest of the apostles. [This do] in the assurance that all these have not run in vain, but in faith and righteousness, and that they are [now] in their due place in the presence of the Lord, with whom also they suffered. For they loved not this present world, but Him who died for us, and for our sakes was raised again by God from the dead." (Letter to the Philippians, Ch. 9)
Both Clement and Polycarp were not just contemporaries but were reported as knowing the apostles. Irenaeus was a student of both men. He tells us that Clement “had seen the blessed apostles, and had been conversant with them,” and that “Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the Church in Smyrna…)” (Irenaeus, Against Heresies, 3.3.3)
"But a clear and unmistakable proof of the fact I hold to be the undertaking of His disciples, who devoted themselves to the teaching of a doctrine which was attended with danger to human life — a doctrine which they would not have taught with such courage had they invented the resurrection of Jesus from the dead; and who also, at the same time, not only prepared others to despise death, but were themselves the first to manifest their disregard for its terrors." (Origen, Contra Celsum Book II, Ch. 56)
Sometimes people will risk death for something false, but not for something that they know to be false without some sort of shot at an earthly reward that makes it worth their while. Rather than offering anything tangible here and now in this life, Christianity promoted giving and loving sacrifice and minimized the importance of earthly power.
In the case of the life of Paul, he lived a single life and worked with his own hands to provide for himself and his traveling companions. He clearly was not motivated by power, sex or money. (1 Corinthians 7:8, 2 Corinthians 4:5, 2 Thessalonians 3:8)
On the significance of their sufferings, from a Jewish scholar:
“… the apostles were willing to suffer for their faith. This is certainly true of Paul, who recounts the suffering he endured, which included being whipped, beaten, stoned, shipwrecked, near starvation and in danger from various people and places (2 Cor. 6:4–9). Speaking for the apostles, after being threatened by the religious leaders, Peter and John say, “For we cannot but speak of what we have seen and heard” (Acts 4:20). The apostles are then thrown in prison, beaten for their faith, but they continued to preach and teach the gospel (Acts 5:17–42)...This does not prove that the resurrection is true. But it shows the depth of the apostles’ convictions. They were not liars. They truly believed Jesus rose from the grave and they were willing to give their lives for it.”
- Dr. Pinchas Lapide, Former Orthodox Jewish theologian, Israeli historian and diplomat. Author of The Resurrection of Jesus: A Jewish Perspective.