My beliefs on this subject are formed and fitted within a "system" that sees apostolic, or New Testament, practice as normative. Those who reject this view may have a hard time identifying with my conclusions.
In the New Testament, apostles, and evidently evangelists, were in the main traveling ministers who had "no certain dwellingplace". Elders or bishops (which were plural in number) were localized teachers identified with a certain congregation. This would account for a need of support on the part of these sent ones that would not be necessary for settled ones. An apostle might be in a place as much as three years or as little as three weeks (at least in Paul's case). One would not be able to put down roots, find a steady job, buy a place, build a home and "set up shop". All these would be a possibility for a settled teacher.
Further I would contend that the modern view of the Baptist pastor who not only preaches but also handles everything from visitation to weddings, funerals, church administration -- maybe even the church cleaning and mowing -- is not based on the New Testament model. The entire congregation is a body with differing gifts (cf. I Cor. 12, Rom. 12:6-8; I Pet. 4:10,11, et al.); it seems that the one job that bishops/pastors have that is specific to the office is teaching the entire congregation. Everybody else also ought to be engaged in the visiting of the sick, etc., etc. If a church cannot be happy unless only the pastors are doing those jobs, they lack at least that much understanding the role of ministry and the true idea of the church as a functioning body.
This New Testament foundation helps make sense of Paul's actions and instructions. For this reason, Paul might defend the right of an apostle to be supported (or even take his wife with him, which would require her support), and yet turn around and tell elders that he has made his own way without charge in order to set an example for them to labor (cf. I Cor. 9:1-14; Acts 20:33-35; II Thess 3:8,9). I Cor. 9 is an important passage that establishes the apostolic right of support. Paul gives a clear argumentation based on several different principles. What also must be clear is that an apostle was not required to enforce that right on the churches.
I Cor 9:1-18 Am I not an apostle? am I not free? have I not seen Jesus Christ our Lord? are not ye my work in the Lord? If I be not an apostle unto others, yet doubtless I am to you: for the seal of mine apostleship are ye in the Lord. Mine answer to them that do examine me is this, Have we not power to eat and to drink? Have we not power to lead about a sister, a wife, as well as other apostles, and as the brethren of the Lord, and Cephas? Or I only and Barnabas, have not we power to forbear working? Who goeth a warfare any time at his own charges? who planteth a vineyard, and eateth not of the fruit thereof? or who feedeth a flock, and eateth not of the milk of the flock? Say I these things as a man? or saith not the law the same also? For it is written in the law of Moses, Thou shalt not muzzle the mouth of the ox that treadeth out the corn. Doth God take care for oxen? Or saith he it altogether for our sakes? For our sakes, no doubt, this is written: that he that ploweth should plow in hope; and that he that thresheth in hope should be partaker of his hope. If we have sown unto you spiritual things, is it a great thing if we shall reap your carnal things? If others be partakers of this power over you, are not we rather? Nevertheless we have not used this power; but suffer all things, lest we should hinder the gospel of Christ. Do ye not know that they which minister about holy things live of the things of the temple? and they which wait at the altar are partakers with the altar? Even so hath the Lord ordained that they which preach the gospel should live of the gospel. But I have used none of these things: neither have I written these things, that it should be so done unto me: for it were better for me to die, than that any man should make my glorying void. For though I preach the gospel, I have nothing to glory of: for necessity is laid upon me; yea, woe is unto me, if I preach not the gospel! For if I do this thing willingly, I have a reward: but if against my will, a dispensation of the gospel is committed unto me. What is my reward then? Verily that, when I preach the gospel, I may make the gospel of Christ without charge, that I abuse not my power in the gospel.
It is well also to understand this passage in context (esp. chapters 8-10) of Paul's argument of placing one's rights below or in subordination to the furtherance of the gospel. As Paul instructs the Corinthians to do so, he gives a specific example showing that he is not asking them to do something he has not done or is unwilling to do; something they very well knew he had done -- serve them without charge. He clearly formulates his "right" in order to show that he had not insisted on it. Also worthy of note is that Paul was not the only one for whom this was the common practice. He cites Barnabas* in verse six. In I Corinthians 12, he indicates that Titus also followed him in this.
II Cor. 12:13-18 For what is it wherein ye were inferior to other churches, except it be that I myself was not burdensome to you? forgive me this wrong. Behold, the third time I am ready to come to you; and I will not be burdensome to you: for I seek not yours, but you: for the children ought not to lay up for the parents, but the parents for the children. And I will very gladly spend and be spent for you; though the more abundantly I love you, the less I be loved. But be it so, I did not burden you: nevertheless, being crafty, I caught you with guile. Did I make a gain of you by any of them whom I sent unto you? I desired Titus, and with him I sent a brother. Did Titus make a gain of you? walked we not in the same spirit? walked we not in the same steps?
And though in I Cor. 9 Paul indicates that Peter and others did accept their maintenance (and even their wives, 9:5), it does not follow that they always did so. I Cor. 4 indicates that other apostles at one time or another labored with their hands. Note that "we" is the subject of the sentence in verse 12, and "apostles" is the antecedent of "we".
I Cor 4:9-12 For I think that God hath set forth us the apostles last, as it were appointed to death: for we are made a spectacle unto the world, and to angels, and to men. We are fools for Christ's sake, but ye are wise in Christ; we are weak, but ye are strong; ye are honourable, but we are despised. Even unto this present hour we both hunger, and thirst, and are naked, and are buffeted, and have no certain dwellingplace; And labour, working with our own hands: being reviled, we bless; being persecuted, we suffer it:
* Side note - it appears this reference to Barnabas occurs after he and Paul had separated (cf. Acts 15:36-41 & 18:1-17)
Here are a few other verses that relate to the subject, plus a comment on elders:
Acts 20:33-35 I have coveted no man's silver, or gold, or apparel. Yea, ye yourselves know, that these hands have ministered unto my necessities, and to them that were with me. I have shewed you all things, how that so labouring ye ought to support the weak, and to remember the words of the Lord Jesus, how he said, It is more blessed to give than to receive.
II Cor. 11:9 And when I was present with you, and wanted, I was chargeable to no man: for that which was lacking to me the brethren which came from Macedonia supplied: and in all things I have kept myself from being burdensome unto you, and so will I keep myself.
I Thess. 2:6-9 Nor of men sought we glory, neither of you, nor yet of others, when we might have been burdensome, as the apostles of Christ. But we were gentle among you, even as a nurse cherisheth her children: So being affectionately desirous of you, we were willing to have imparted unto you, not the gospel of God only, but also our own souls, because ye were dear unto us. For ye remember, brethren, our labour and travail: for labouring night and day, because we would not be chargeable unto any of you, we preached unto you the gospel of God.
II Thess. 3:7-9 For yourselves know how ye ought to follow us: for we behaved not ourselves disorderly among you; Neither did we eat any man's bread for nought; but wrought with labour and travail night and day, that we might not be chargeable to any of you: Not because we have not power, but to make ourselves an ensample unto you to follow us.
Several verses of Scripture indicate that plurality of elders was the norm in the New Testament churches (e.g. Acts 11:30; 13:1; 14:23; 15:2ff; 20:17; Philipp. 1:1; I Thess. 5:12; Titus 1:5; James 5:14). These thoughts of mine do not hinge on the fact that there must be a plurality of elders. But if one understands that such as plurality was the norm in the churches in New Testament times, it should at least call for a re-thinking of whether these churches would have supported all these men as full time paid pastors according to the modern concept of such. The holding of all things common, as practiced in the Jerusalem church, should also at least give pause. Though this was evidently only practiced in that one church (and therefore not normative for all churches), the fact that during this time all were supported equally (apostles, elders, and members) should make us wonder whether the early church had any concept of holding anyone up for special support above all others based simply on office and not need.