Does Acts 20:33-34 suggest that a church should not have a paid ministry? 33 I have coveted no man’s silver, or gold, or apparel.

34 Yea, ye yourselves know, that these hands have ministered unto my necessities, and to them that were with me.
No, it does not.  A common mistake is to take a particular situation or statement by one person and attempt to apply it as a rule to all situations.  All this passage means is that Paul worked to provide for his own living while he lived among the Ephesians.  Paul did accept provision from others in other cities and at other times.  The book of Philippians is in many ways a thank you letter for gifts given.


  Yet it was kind of you to share my trouble. 15 And you Philippians yourselves know that in the beginning of the gospel, when I left Macedonia, no church entered into partnership with me in giving and receiving, except you only. 16 Even in Thessalonica you sent me help for my needs once and again. 17 Not that I seek the gift, but I seek the fruit that increases to your credit.  Philippians 4:14-17 ESV


He speaks to this again in his first letter to the church in Corinth:


  Or is it only Barnabas and I who have no right to refrain from working for a living? 7 Who serves as a soldier at his own expense? Who plants a vineyard without eating any of its fruit? Or who tends a flock without getting some of the milk?  Do I say these things on human authority? Does not the Law say the same? 9 For it is written in the Law of Moses, “You shall not muzzle an ox when it treads out the grain.”  1 Corinthians 9:6-9 ESV


So, no, this is not a universal principle that no one should ever receive his living from those to whom he ministers.  It merely records that a minister does not have to do this, and Paul, in particular, did not do this during one specific place in his ministry, though he did receive compensation elsewhere.