Is there any type of paint that should not be painted over using Valspar Stormcoat Satin Latex? I’m not sure of what type of paint was used before.

No, you should be fine with applying this product over your current finish. Remove all wax, grease, dirt, chalk, mildew, loose and peeling paint, and other foreign matter. Remove gloss from shiny surfaces. Fill all cracks and joints with Acrylic caulk before top coating. Remove any dust and efflorescence. New or bare surfaces should be primed with an appropriate Valspar primer.