Set print quality to ‘Best’ by default

You define your settings and then save them as a custom preset in the Presets drop-down (Save Current Settings as Preset…).

After selecting your preset and printing once, the preset is remembered in all applications that use the standard print dialog.

Just make sure the Reset Presets Menu to "Default Settings" After Printing checkbox is unchecked in the Presets window/dialog (Show Presets… in the drop-down), which it should be by default.