There's a noticably different focus on this matter if you read Paul's letters and those of the other apostle's seperately.
The Apostle Paul preached heavily about Grace and Faith.
The other apostles still placed more emphasis on law and works as necessary for salvation
The emphasis on works/faith is one of the noticeable differences. I personally think that difference comes from that fact that Paul was chosen by the Lord even though he was extremely opposed right up to his conversion. He hadn't done one good work up to that point (from a Christian point of view), but was still chosen to play a large part in developing early Christianity.
Another example is that It was the Jewish apostles who decided on the additional "necessary things" to abstain from (including meat sacrificed to idols) [Acts 15:28,29] in order to keep the peace between the Jewish and Gentile Christians. Paul in 1 Cor 8 and 10, pointed out that abstaining from meat sacrificed to idols wasn't in fact necessary, but it was good to avoid so as not to stumble ones sensitve to the issue. Then in Revelation, written by Peter, he condemns one congregation for eating things sacrificed to idols.
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The scripture about not going from door-to-door was referring to finding lodging. They were supposed to stay at the first home they were accepted at until they finished preaching in that city.