Historically, it seems that the Romans would use crucifixion for the worst criminals and especially for non-Romans. Since Christ had angered the religious leaders at the time by His preaching, saying that the temple would be destroyed (Mark 13.2), and also throwing the moneychangers out of the temple (Mark 11.15-18), they appealed to Pilate and petitioned for Christ to be treated as a criminal. There was also a huge crowd clamoring for Christ to be crucified when Pilate presented him, so Pilate agreed to do so but washed his hands of it.
From another angle, Christ being crucified as if He were the worst of criminals was part of the Condescension of God, and was a necessary part of His sacrifice. He descended to the lowest of the low to afterwards be exalted. His crucifixion also fulfills some prophecies and symbols from the scriptures, such as the bronze serpent that Moses lifts up to heal the Israelites (Numbers 21.8).
Interestingly enough, there’s also a part of the Law of Moses that says that anyone who committed a sin worthy of death should be hanged on a tree (Deuteronomy 21.22). The cross could represent a tree, showing that Christ really descended to the depths of misery and suffering as part of His condescension. It’s also a symbol of how Christ becomes our intercessor by taking our sins upon Him (Galatians 3.13).