The Prosperity of the Gospel comes down to a matter of the heart: Do you have wealth, or does wealth have you?
Prosperity in the Modern Church
Often viewed as the "Father of the Prosperity Movement", Kenneth E Hagin often pointed to passages such as Matthew 7:11, reading,
If you, then, though you are evil, know how to give good gifts to your
children, how much more will your Father in heaven give good gifts to
those who ask him!
Matthew 7:11
Kenneth Hagin's point was that it was on the basis of Faith by which men petitioned heaven for all types of requests, both for one's self and for others, and it was on the basis of God being a Good Father that He would do it, even so much more than an evil father would. Saying, "What father wouldn't work himself to the bone to see that his child had a better life than he did."
Often beginning with these two texts, he explained these exactly as written,
Truly I say to you, whoever says to this mountain, ‘Be taken up and
cast into the sea,’ and does not doubt in his heart, but believes that
what he says is going to happen, it will be granted him. Therefore I
say to you, all things for which you pray and ask, believe that you
have received them, and they will be granted you.
Mark 11:23-24
And,
If you remain in me and my words remain in you, ask whatever you wish,
and it will be done for you. This is to my Father’s glory, that you
bear much fruit, showing yourselves to be my disciples.
John 15:7-8
His message that if one simply asked God with simple faith, believing, like the Scriptures said, without doubt, it would be granted. And, through his own experiences with health, he claimed to have tested and proved it.
Prosperous, not Covetous
Kenneth Hagin said that God doesn't mind his people being prosperous, so long as they're not covetous. The issue was the heart, and having a right relationship with God first, from which God would then supply our needs. He points out how, in his language, that the Lord began to ask him what the world and all of its things were created for. And, that God had originally created the world for his man Adam, to use and enjoy. Following this line, God told him that as he learned to listen and rely on His leading, He would make Mr. Hagin "rich". Hagin differentiated "rich" from a "millionaire" by defining "rich" as "abundant supply".
While he was the father of this movement, according to many, he also published The Midas Touch towards the end of his ministry (2002), warning people not to become "money minded".
Following the logic of the arguments, it can be noted that many if not most churches in modern countries own their own buildings, support their own pastors, and those pastors are supplied for in varying degrees. One must also remember, in keeping with Jesus' words of the "wheat" and the "tares", that people will always take things to extremes.
The argument for the prosperity Gospel is simply that if God wanted us in destitute poverty, with absolutely nothing, the Scripture contradicts (Paul rented his house in Acts 28 with some form of money, and people clearly gave a portion of their income elsewhere). The question could then progress to how much does God want you to have? To which, the Scriptures are in fact silent.
Further Support
But, the argument for Prosperity with the Gospel, when approached with integrity, has more to do with supply than it does with greed.
“Truly I tell you,” Jesus replied, “no one who has left home or
brothers or sisters or mother or father or children or fields for me
and the gospel will fail to receive a hundred times as much in this
present age: homes, brothers, sisters, mothers, children and
fields—along with persecutions—and in the age to come eternal life.
Mark 10:29-30
In the above passage, while not disagreeing with passages such as Luke 14:33 which say we must leave everything, but agrees that there is some form of return, somehow. Although persecutions will come with it, the passage clearly indicates that it will be received 100-fold, in this life as well as the next.
Paul's Approach
In this way, we might also detect a bit of both the opportunity and possibilities with God. In the reading of Paul, we see he willingly forwent a salary (at least at times), because he preached out of compulsion before God--God mandated that he do it. So, he forewent wealth so that he might have a reward from his preaching. One could further the conjecture, based upon his writings in 1 Corinthians 4 and 2 Corinthians 11-12 and various places, that it is the right of the Christian to have all the full measure of what Christ should have been afforded.
Paul, in 1 Corinthians 4:9, says that those who man would consider to be "first" (the apostles) were led around "like those condemned to die". In retrospect, looking at Paul's "boastings" in 2 Corinthians 11-12, we see Paul relating all of his hardships. One could read the passages as saying, "By my right in Christ, I have right to all the blessings that Christ should have had, and was cut short in--including wealth, prosperity, health, comfort, and peace. Instead, I get hard-ships, beatings, mockings, rejection, fastings, sleepnessness, and the like, and it is in this that God's ability shines through the greatest. When I am weak, then I am strong, and it is God showing up through me that brings salvation to you."
But he said to me, “My grace is sufficient for you, for my power is
made perfect in weakness.” Therefore I will boast all the more gladly
about my weaknesses, so that Christ’s power may rest on me. 10That is
why, for Christ’s sake, I delight in weaknesses, in insults, in
hardships, in persecutions, in difficulties. For when I am weak, then
I am strong.
2 Corinthians 12:9-10
Paul appears to say that though he has all the rights to the blessed good life, he willingly foregoes them for the same reason of Christ, to save souls. His conclusion in this matter, above, echoes what Christ said in the Sermon on the Mount.
[Most Happy] are those who are poor in Spirit, for theirs is the
Kingdom of Heaven.
Matthew 5:3
"His strength being made perfect in weakness", that while Paul was entitled to material prosperity, it was through weakness that God worked the most powerfully.
Conclusion
In the case of Kenneth E Hagin, his primary focus was obedience to God's word, and the purpose of the wealth he received was to further the Kingdom. In the case of Paul, the same would be true.
The case for prosperity, then, stretches from Adam in the garden, through this life, and into eternity (Mark 10:30). It includes losing all, but its focus is on seeking first God's Kingdom (Matthew 6:33).
Of course, there are variations. If the above holds true and is correct, the presence of the false, or people who take it too far or too short certainly does not preclude the validity of the foregoing. Rather, with any Biblical truth, where there is truth to be found, people generally are people and usually find a way to distort it, including the topic of wealth.
Other people would certainly have different approaches, but the above holds more or less true across the New Testament, taking into account a variety of verses on both sides, while keeping the main thing the main thing, as far as I can account for it.