To see an encoded AM radio wave, what kind of Oscilloscope do I need?
Your highest frequency of interest is 1.6 MHz.  That is "low" for ordinary oscilloscopes.  Just about any scope can go up to 10 MHz.  There is really nothing here any regular oscilloscope can't do.

Analog scopes today are only for specialty niche applications.  Yours isn't one of them.  A digital scope will serve you better.  The drawbacks you claim for digital scopes are nonsense, especially for this application.