The data architect should recommend Lighting platform plus license type for the finance team that best meets the requirements. This license type allows users to access custom objects and run reports and dashboards on them, without accessing any sales objects. Option A is incorrect because Service Cloud license type is more suitable for customer service users who need to access cases, knowledge, and other service objects. Option B is incorrect because Sales Cloud license type is more suitable for sales users who need to access accounts, contacts, opportunities, and other sales objects. Option C is incorrect because Light Platform Start license type does not allow users to run reports and dashboards on custom objects.