Why do Tom and Joe run away, what do they take with them, where do they run, and why do they begin to feel guilty?

Tom decides to run away "to escape from hard usage and lack of sympathy at home".  He has been downhearted because of the murder he witnessed, and because Becky Thatcher has not been at school, and his Aunt, thinking he has been sick, has unsympathetically been making him take some nasty "Painkiller".  Then, when Becky returns to school, she first ignores Tom then treats him with disdain.  Tom is running away to get back at them.

Joe is running away for similar reasons.  His mother has whipped him for something he says he didn't do, and he is angry.  Tom and Joe decide to become pirates, and invite Huck Finn along.  They will meet on the riverbank two miles above the village, take a raft, and row over to Jackson Island on the Mississippi.  Each boy will bring hooks and lines, and whatever he can steal.  Tom brings a boiled ham and "a few trifles", Joe brings a side of bacon, and Huck brings a skillet, some leaf tobacco, and corncobs with which to make pipes.  As the boys, having settled on the island, fall asleep, Tom and Joe begin to feel guilty about running away, and about stealing the meat and other things (Chapter 13).