Actually, it seems that all three are true.
Some, such as Satan and his evil angels, the Antichrist and the False Prophet and those who take the Mark of the Beast, will face eternal punishment. Their's is a devastating evil that must be confined and destroyed continuously and there will be no possible escape from the Lake of Fire. It is important to remember that angels live forever--they are not mortals. The evil angels who are confined in the "bottomless pit" are still alive and just waiting to be released (perhaps they already have been). Those foolish men and women who voluntarily take the Mark of the Beast will likely be enticed by the idea of immortality--which may be the promised result. They will have missed the "small print" which tells them that they will gain immortality but that just means living forever in horrific punishment and eternal death. They could have had eternal life with Father God and the Lamb and they will learn, to their chagrin, that they could have chosen that instead of Satan's way.
Those who are just "ordinary" ignorant mortals and prone to be fleshly and worldly because of this world, which is dominated by Satan will likely be granted some measure of mercy. Jesus begged the Father to "Forgive them for they know not what they do." And we have no reason to believe that the Father would deny that prayer--that they will not be given the mercy of oblivion after their punishment is done. They will be destroyed in the Lake of Fire--the Second Death.
Finally, there is, of course, no punishment at all for believers. The Roman Catholic notion of purgatory is nonsensical. One will either be in heaven or not--no matter what kind of sin has been forgiven under the Blood of Christ. The so-called "thief on the cross" (actually, it is likely that he was some kind of political zealot who had, perhaps, murdered Romans) said he and the criminal on the third cross deserved to die--unlike Jesus. He was told by Jesus that he would be in Paradise after his death--not, purgatory. The notion of "purgatory" is saying that the Blood of Jesus is insufficient to pay for any and all sin and is quite blasphemous.