C# – Disable default cell selection in datagridView

I think that this is what you're looking for. But if not, hopefully it will give you a start.

private void dataGridView1_SelectionChanged(object sender, EventArgs e)
{
    DataGridView dgv = (DataGridView)sender;

    //User selected WHOLE ROW (by clicking in the margin)
    if (dgv.SelectedRows.Count> 0)
       MessageBox.Show(dgv.SelectedRows[0].Cells[0].Value.ToString());

    //User selected a cell (show the first cell in the row)
    if (dgv.SelectedCells.Count > 0)
        MessageBox.Show(dgv.Rows[dgv.SelectedCells[0].RowIndex].Cells[0].Value.ToString());

    //User selected a cell, show that cell
    if (dgv.SelectedCells.Count > 0)
        MessageBox.Show(dgv.SelectedCells[0].Value.ToString());
}

You can use the CellMouseEnter and CellMouseLeave to track the row number that the mouse is currently hovering over.

Then use a ContextMenu object to display you popup menu, customised for the current row.

Here's a quick and dirty example of what I mean...

private void dataGridView1_MouseClick(object sender, MouseEventArgs e)
{
    if (e.Button == MouseButtons.Right)
    {
        ContextMenu m = new ContextMenu();
        m.MenuItems.Add(new MenuItem("Cut"));
        m.MenuItems.Add(new MenuItem("Copy"));
        m.MenuItems.Add(new MenuItem("Paste"));

        int currentMouseOverRow = dataGridView1.HitTest(e.X,e.Y).RowIndex;

        if (currentMouseOverRow >= 0)
        {
            m.MenuItems.Add(new MenuItem(string.Format("Do something to row {0}", currentMouseOverRow.ToString())));
        }

        m.Show(dataGridView1, new Point(e.X, e.Y));

    }
}