Can I buy an OpenType font (New Century Schoolbook) on Adobe's website, or do I have to go elsewhere?

Unfortunately, not directly.

As explained at Fonts by Adobe, FAQ | Adobe, you can license such fonts via third parties such as Fontspring at Adobe | Fontspring.

Only the “Adobe Originals” fonts are so licensable. For fonts in the Adobe Library from other sources such as Monotype, Linotype, and ITC, you will need to go those vendors or other resellers directly.

Adobe also offers the Typekit “fonts by subscription” service. See http://typekit.com.

         - Dov