Radio

enum SingingCharacter { lafayette, jefferson }

// ...

SingingCharacter _character = SingingCharacter.lafayette;

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