Ionic + Ionic material is the best choice.
Angular Material + Ionic are fairly incompatible (you can add them to the same project, but the styling will be extremely inconsistent and none of the UI components will work cross-framework, eg. an ionic side menu with material tabs). Ionic is 1.0 and angular material is still pre-1.0.
It's better to use ionic framework and ionic material together as ionic material is a "material extension" to Ionic.
Ionic Material extends the actual ionic framework namespace (in JS), renders material styles on the ionic elements (following ionic's conventions), and will aim to follow the releases of Ionic, and support material theming, ink, and motion for any new Ionic release, which explains why ionic material + angular would not be a great choice either.
Link poster by machnicki explains it all.