RadioListTile

enum SingingCharacter { lafayette, jefferson }

// ...

SingingCharacter _character = SingingCharacter.lafayette;

@override
Widget build(BuildContext context) {
  return Column(
    children: <Widget>[
      RadioListTile<SingingCharacter>(
        title: const Text('Lafayette'),
        value: SingingCharacter.lafayette,
        groupValue: _character,
        onChanged: (SingingCharacter value) { setState(() { _character = value; }); },
      ),
      RadioListTile<SingingCharacter>(
        title: const Text('Thomas Jefferson'),
        value: SingingCharacter.jefferson,
        groupValue: _character,
        onChanged: (SingingCharacter value) { setState(() { _character = value; }); },
      ),
    ],
  );
}