1. Right click the DataGridView and select Edit Columns

    Edit Columns

  2. Select the DefaultCellStyle Property and click on the Style Wizard

    DefaultCellStyle

  3. In the CellStyle Builder window, you can set whatever properties you'd like, including BackColor

    CellStyle Builder

What this will do is set the property inside of the form.designer.cs file during InitializeComponent()

private void InitializeComponent()
{
    /// ...
    this.ShadedColumn.DefaultCellStyle.BackColor = Color.Silver;
    /// ...
}

<sup>* where this.ShadedColumn is the name of the DataGridViewTextBoxColumn control you added</sup>

Any code in InitializeComponent will execute during the designer view, and technically you can update most styles directly here, but it's advised to use the GUI form builder to make any changes against this file

Further Reading: Set Default Cell Styles and Data Formats for the Windows Forms DataGridView Control Using the Designer