如何正确将DataGrid中的ComboBox绑定到ViewModel的List或Enum？

我尝试在DataGrid的ComboBox列中让用户选择选项，先后用了Binding和x:Bind两种方式，但一开始的代码无法正常工作——我原本觉得逻辑没问题，实际却存在问题。初始代码如下：

初始代码 #

ViewModel #

public partial class CustomerModel : ObservableObject
{
    private ObservableCollection<DataType> _objects;
    public ObservableCollection<DataType> Objects
    {
        get => _objects;
        set => SetProperty(ref _objects, value);
    }

    private ObservableCollection<string> _field;
    public ObservableCollection<string> Field
    {
        get => _field;
        set => SetProperty(ref _field, value);
    }


    public CustomerModel()
    {
        Objects = new();
        Field = new ObservableCollection<string> { "Test", "Test" };
    }


    public class DataType : ObservableObject
    {
        public int ID { get; set; }
        public string Name { get; set; }
        public string Caption { get; set; }
        public bool Numeric { get; set; }


        public DataType()
        {

        }
      
    }
}

XAML #

<controls:DataGrid
    x:Name="dataGrid1" KeyDown="dataGrid1_KeyDown"
    ItemsSource="{x:Bind Model.Objects}" AutoGenerateColumns="False" >
    <controls:DataGrid.Columns>
        <controls:DataGridComboBoxColumn Header="Field" ItemsSource="{x:Bind Model.Field}" Tag="Field"/>
    </controls:DataGrid.Columns>
</controls:DataGrid>

更新后的可运行代码 #

现在我写出了能正常运行的更新代码，想请教这段代码是否合理：

ViewModel #

public partial class CustomerModel : ObservableObject
{
    
    public enum Choices { A, B, C }
    [ObservableProperty]
    private ObservableCollection<DataType> _objects;
    

    public CustomerModel()
    {
        Objects = new();
        var data = new DataType();
        Objects.Add(data);
  
    }
    public static Choices[] ChoicesOptions { get; } = Enum.GetValues<Choices>();


    public partial class DataType : ObservableObject
    {
        public int ID { get; set; }
        public string Name { get; set; }
        public string Caption { get; set; }
        public bool Numeric { get; set; }

        [ObservableProperty]
        private Choices _choice;
    }
}

XAML #

<controls:DataGridComboBoxColumn Header="Field" Binding="{Binding Choice}" ItemsSource="{x:Bind local:CustomerModel.ChoicesOptions, Mode=OneTime}" Tag="Field"/>

额外疑问 #

另外我注意到有人会在后台代码中实例化ViewModel，请问这是否必要？我的后台代码如下：

public sealed partial class DataGridPage : Page
{
    public DataGridPage()
    {
        this.InitializeComponent();
    }
}

内容的提问来源于stack exchange，提问作者miniHessel