This was a time of delivering the message of the Messiah that Israel hoped for. If they rejected him as Messiah then they were to be rejected. This was to be illustrated by the knocking off of the dust. In other words he so strongly DIDN'T want anything to do with them that even their dirt wasn't worthy to touch the bottom of their feet.
(Matthew 10:32-33 KJV) Whosoever therefore shall confess me before men, him will I confess also before my Father which is in heaven. {33} But whosoever shall deny me before men, him will I also deny before my Father which is in heaven.
Also, he sent them out without any provisions because the priests (Levites) were to be cared for by the people they ministered to. In this case the people would prove their receiving of the disciples by providing for them. In addition to this, it was so the disciples would see many miracles of how God was caring for them.
Later he changed the instructions on how they were to accomplish their mission to include the suffering they would be receiving. It was their privelege to suffer with Christ since they were going to reign with him.
(Luke 22:35-38 NIV) Then Jesus asked them, "When I sent you without purse, bag or sandals, did you lack anything?" "Nothing," they answered. {36} He said to them, "But now if you have a purse, take it, and also a bag; and if you don't have a sword, sell your cloak and buy one. {37} It is written: 'And he was numbered with the transgressors' ; and I tell you that this must be fulfilled in me. Yes, what is written about me is reaching its fulfillment." {38} The disciples said, "See, Lord, here are two swords." "That is enough," he replied.
It's interesting to note that this section of scripture also provides biblical support for owning weapons for the purpose of protection.