Memo1.Lines.Add('еще одна строка'); 

procedure TForm1.Button1Click(Sender: TObject);
var
  new_x, new_y, i: integer;
begin
  new_x := 0;
  new_y := 1;
  i := SendMessage(Memo1.Handle, EM_LINEINDEX, new_y, 0) + new_x;
  SendMessage(Memo1.Handle, EM_SETSEL, i, i);
  Memo1.SetFocus;
end;

type
    TCM = class(TCustomMemo);
//...
procedure TForm1.Button1Click(Sender: TObject);
var
  new_caret_pos: TPoint;
begin
  new_caret_pos.X := 5;
  new_caret_pos.Y := 1;
  TCM(Memo1).SetCaretPos(new_caret_pos);
  Memo1.SetFocus;
end;