For completness of this question, better to use a Grid event rather than mouse.
First Set your datagrid properties:
SelectionMode to FullRowSelect and RowTemplate / ContextMenuStrip to a context menu.
Create the CellMouseDown event:-
private void myDatagridView_CellMouseDown(object sender, DataGridViewCellMouseEventArgs e)
{
if (e.Button == MouseButtons.Right)
{
int rowSelected = e.RowIndex;
if (e.RowIndex != -1)
{
this.myDatagridView.ClearSelection();
this.myDatagridView.Rows[rowSelected].Selected = true;
}
// you now have the selected row with the context menu showing for the user to delete etc.
}
}