Though the Portuguese were the first to begin colonization and trade in slaves in West Africa, they were later unified with Spain. During the unification, Portugal was officially barred from engaging in the slave trade. This unification came in 1580, so for the purposes of this question, I will consider Portugal as part of Spain.
The four Western European nations most greatly involved in the West African colonization and slave trade were Spain, England, France, and the Netherlands. All four of these nations were involved in the Trans-Atlantic trade of goods and people. The people captured in Africa were primarily transported to other colonies of their captors for the purpose of laboring in the production of exportable goods and raw materials. While most captured slaves were taken to the Americas and Caribbean Islands, a small portion were taken to mainland Europe to be sold.