What were the common characteristics of initial encounters between Europeans and Native Americans?
The most important things that were common to most initial contacts between Native Americans and Europeans was a certain amount of bewilderment on the part of the Native Americans and a certain sense of arrogance and entitlement on the part of the Europeans.
Most Native Americans did not know exactly what to make of the Europeans. They did not have any experience with people who were physically so unlike them and had such strange cultures. The Europeans' advanced technology added to the difficulty that the Native Americans had in understanding them.
The Europeans, on the other hand, had none of these uncertainties. They were well aware that people who were different than them (Africans, Asians) existed. They had the technological superiority. These things made them much more sure of themselves. In addition, these factors and others (like Christianity) gave them a sense that they were better than the Native Americans and were entitled to act as if they had a right to dominate those people.
These were the factors that were common to most initial encounters between Native Americans and Europeans.
One of the great cultural divides was on land tenure. The Native American understanding of land use and authority differed from that of Europeans. When native people "sold" land to Europeans like the so called purchase of the island of Manhattan, they were offering use rights and not property rights in the European sense. Thus when they were chased off the land by Europeans that they thought was to be shared, they grew resentful of European perfidy, while the Europeans came up with cultural misunderstandings of Native behaviors as "Indian giving".
Europeans and natives misunderstood each other's associations and political relationships. Native peoples didn't always understand that attacks on one village could produce a larger reaction from European settlers of the same nationality, while European retaliatory attacks often hit innocent villages not involved in conflicts with Europeans, thus enlarging hostilities.