In the first aliyah, G-d initially leads the Jews in a round about way for two reasons: first was to avoid an immediate war with the Philistine nation (which was on a more direct route) which might cause the Jews to regret leaving Egypt. Second, to appear to be lost to the Egyptians, so they will be encouraged to pursue after them.
Moshe takes the bones of Yosef with him as Yosef had made them promise to do when their redemption came. They were led by G-d, by day in a pillar of cloud, and by night by a pillar of fire.
Pharaoh and the Egyptians regretted letting them leave (Rashi says: because of the money the Jews took that their Egyptian neighbors freely gave them as they left) and pursued after them 600 chariots strong.