How do I know which base my specific mattress needs?

Start with the mattress type. Innerspring mattresses are flexible about their base and work on a traditional box spring, foundation, or platform. Memory foam and hybrid mattresses need a rigid surface: a solid foundation, a platform, or slats spaced 3 inches or less, never an old coil box spring. When in doubt, the mattress maker specifies the required support, and following it keeps both the comfort and the warranty intact.