Will the dead in Christ rise first?
Yes. Scripture plainly teaches that the dead in Christ will rise first, and then those believers still living on earth will be caught up together with them to meet the Lord in the air.
The clearest statement on this is found in 1 Thessalonians 4:16-18, which says the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God, and the dead in Christ shall rise first. Then those who are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air, and so shall we ever be with the Lord.
This order is explained further through the resurrection teaching found in 1 Corinthians 15. The body is sown in corruption but raised in incorruption, sown in weakness but raised in power, sown a natural body but raised a spiritual body. At the last trump, the dead shall be raised incorruptible, and the living shall be changed in a moment, in the twinkling of an eye. Death is swallowed up in victory at that moment, and the sting of death and the victory of the grave are undone.
The bodies of those who have believed and received the atonement of Jesus Christ will rise from the grave and be changed into bodies like unto the glorious body of Christ. Jesus brings their souls back with him to occupy their changed bodies. They rise first, and only after that are the bodies of those still alive at the coming of the Lord changed. In this way, both groups together meet him in the air, exactly as the order in 1 Thessalonians describes.
John 5:28-29 confirms that all who are in the graves shall hear the voice of the Son of man and come forth, those who have done good unto the resurrection of life. This resurrection of the righteous dead is tied to the same hope Paul describes in Philippians 3:21, where the vile body is changed and fashioned like unto Christ's glorious body, whether that body is sleeping in the grave or still alive upon the earth at his coming.
The scriptures
For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first: Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord. Wherefore comfort one another with these words.
In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed. For this corruptible must put on incorruption, and this mortal must put on immortality. So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory. O death, where is thy sting? O grave, where is thy victory?
So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption: It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power: It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body.
And hath given him authority to execute judgment also, because he is the Son of man. Marvel not at this: for the hour is coming, in the which all that are in the graves shall hear his voice, And shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation.
For our conversation is in heaven; from whence also we look for the Saviour, the Lord Jesus Christ: Who shall change our vile body, that it may be fashioned like unto his glorious body, according to the working whereby he is able even to subdue all things unto himself.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.