1 Corinthians 15 touches on the nature of resurrected bodies, making a contrast between earthly bodies and heavenly bodies:
40 There are heavenly bodies and earthly bodies, but the glory of the heavenly is of one kind, and the glory of the earthly is of another. 41 There is one glory of the sun, and another glory of the moon, and another glory of the stars; for star differs from star in glory.
42 So is it with the resurrection of the dead. What is sown is perishable; what is raised is imperishable. 43 It is sown in dishonor; it is raised in glory. It is sown in weakness; it is raised in power. 44 It is sown a natural body; it is raised a spiritual body. If there is a natural body, there is also a spiritual body. 45 Thus it is written, “The first man Adam became a living being”; the last Adam became a life-giving spirit. 46 But it is not the spiritual that is first but the natural, and then the spiritual. 47 The first man was from the earth, a man of dust; the second man is from heaven. 48 As was the man of dust, so also are those who are of the dust, and as is the man of heaven, so also are those who are of heaven. 49 Just as we have borne the image of the man of dust, we shall also bear the image of the man of heaven.
[1 Cor 15:40-49, ESV]
The passage is very clear and unambiguous in stating the fact that Jesus ("the last Adam") became a life-giving spirit (v45). Other translations translate it as quickening spirit, but a spirit in any case. And the surrounding context supports the same obvious conclusion: Jesus' resurrected body was a glorious, heavenly, spiritual body.
We find a similar idea in 2 Cor 3:17 (ESV):
17 Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom.
And the same is said of angels in Hebrews 1:14:
Are they not all ministering spirits sent out to serve for the sake of those who are to inherit salvation?.
(*) Related question about angels: How should we understand the nature of angels in light of Hebrews 1:14 and 13:2?.
However, in Luke 24:39 Jesus makes a claim that, at face value, appears to contradict what we have concluded above:
39 See my hands and my feet, that it is I myself. Touch me, and see. For a spirit does not have flesh and bones as you see that I have.” [Luke 24:39, ESV]
Is there any contradiction? How can Jesus be a life-giving spirit and not a spirit? How to reconcile these seemingly contradictory claims?