Yes, you can put your Saatva Classic on a platform bed, as long as it has a solid surface or horizontal slats spaced less than 4 inches apart. Queen and larger sizes also need proper center support.
Either the 11.5" or 14.5" height can be used with a platform. We recommend the 11.5" version if your platform has a low headboard, so that more of the headboard remains visible. But the decision is purely aesthetic; both mattresses have the same coil count and deliver the same level of comfort and quality. Need more help choosing a mattress height? See How to Choose the Right Mattress Height for You.