The stated purpose of the Spanish in the Americas was "God, gold, and glory." They hoped to find gold and other riches which could be sent back to Spain, and almost incidentally convert the Indians to Christianity. Settlement was not a major concern of the Spanish, although many established large farming/mining concerns under the Encomienda system under which they had government permission to enslave the Indians within their area. They treated the Indians with manifest cruelty, resulting in the first successful revolt in America, namely Pope's Rebellion in which Indians drove out a number of Spanish from the New Mexico area.
The English came to establish true colonies, a source of raw materials for England and also a source of markets for manufactured goods. Most were settled by joint stock companies or other investment entities with the hope of economic profit; although all soon became royal colonies under the control of the Lords of Plantation and Trade.
The French also came to profit economically and perhaps also Christianize the Indians. Their primary concern was the Fur trade. They had better relations with the Indians than any of the others; in fact many French settlers married Indian wives and adopted Indian clothing and customs. However, they were strictly Roman Catholic. When France lost its North American possessions after the Seven Years War, the French King ordered all colonists to abandon the area. Many ignored his command.
The Dutch who settled New Amsterdam were there solely to promote their mercantile empire. At the time, they had the largest commercial fleet in Europe, and its colony was primarily to support that fleet. The Dutch surrendered New Amsterdam to the English in exchange for concessions in the Spice Islands of Indonesia.