An account represents an organization or customer relationship. A contact is a person, usually related to an account. A lead holds an unqualified prospect; conversion can connect that prospect to an account and contact and optionally create an opportunity. An opportunity tracks a potential sale. A case tracks a service request.
Choose the object from the work being managed. A customer can have an open opportunity and an unresolved case at the same time, because those records answer different questions. Creating another account to represent a support request hides that distinction. Before converting a lead, search for an existing account and contact. Duplicate names are possible, so use identifiers and verified matches when a relationship matters.