Jesus sent out the Apostles on their own to preach the Gospel of the Kingdom to folks in the region of Galilee (Luke 9:2). Sending them out two-by-two (Mark 6:7) was necessary for the Twelve to learn to do these things by themselves, because Jesus wouldn’t always be there to do the preaching. They had to learn to do what Jesus did. Therefore, Jesus gave them authority over demons and diseases and power to work miracles etc. as signs to show that the word they preached was true (Luke 9:1).
Jesus wanted to teach the disciples to depend upon the Lord for their needs, so he told them not to bring staffs, or a (beggar’s) bag, or bread, or money or even two (inner) garments (Luke 9:3).
The fact that Mark tells us that a staff was permitted for the journey has presented a problem for many Bible students who sought to harmonize the Synoptics, but Mark really doesn’t contradict Luke. All we need to do is remember that what Jesus said in Aramaic or Hebrew was translated into the Greek. The Greek word for staff(s) is rhabdos (G4464). It is the only word in the New Testament that is used for a staff or rod of any kind. The Septuagint uses this same Greek word for seven different Hebrew words: H2415; H4294; H4731; H4938; H6086; H7626; H8275. Aaron’s staff (H4294), for example, was used for walking, but the rod (H7626) was used for discipline (Exodus 21:20) and protection (Psalm 2:9; 23:4), but the same Greek word (G4464) is used for both in the Septuagint. So, taking a walking stick or staff (G4464) for their journey would be permitted (Mark 6:8), but to take a rod or club (G4464) for protection wouldn’t be appropriate for the context of depending upon God for ones welfare (cf. Luke 9:3).
Jesus told the disciples to stay in one house for the entire time they were in any given town (Luke 9:4), because he didn’t want them to give the impression that they sought better accommodations. That sort of thing would be a breach of etiquette in ANE culture and would reflect disparagingly upon the Gospel of the Kingdom.
The Apostles could probably expect to be about as successful as Jesus. Some people rejected Jesus outright, so the disciples could expect the same attitude from some folks toward them, because they taught in Jesus’ name (Luke 9:5). If some towns in Galilee refused to offer hospitality to the Apostles, the disciples were to shake off the dust of that city that clung to their sandals and clothes, and such an act would be a witness against the Jews of that city (cf. Acts 13:14, 50-51; 18:1-6). The meaning of this act is tied to the Jewish understanding that the soil of gentile lands was unclean:
“For it was taught, Jose b. Jo’ezer of Zeredah and Jose b. Johanan of Jerusalem decreed uncleanness in respect of the country of the heathens” [Babylonian Talmud: Shabbath, folio 14b – emphasis mine; footnotes are in the original].
Therefore, if this act was performed in the presence of a Jew, it would be understood that the disciples considered those refusing the Gospel to be as unclean as any gentile or their town was as unclean as any gentile town (Luke 9:5; cf. Nehemiah 5:13).
The Twelve went out and did as Jesus had instructed them, preaching the Gospel and healing those in need, wherever they were found (Luke 9:6), and after a short time (two or three weeks) they returned to Jesus and told him all they said and did (Luke 9:10; cf. Mark 6:30), proving to themselves and those who would follow that Jesus’ authority can be delegated to others, and, when it is, Jesus’ disciples will be able to do as Jesus did, as they proclaim the good news of the Kingdom of God (Luke 9:2).
 A town in Persia
 Two Rabbis of the early Maccabean period (second century BC); together they formed the beginning of the Zugoth (duumvirate), which governed Jewish religious life until Hillel and Shammai.