My task mode column is not showing up by default when I create a new project

Andy --

The Task Mode column only shows up by default in only a few task tables, the most notable of which is the Entry table.  I suspect you are not seeing the Task Mode column by default because you upgraded from Microsoft Project 2003 or 2007 to either Microsoft Project 2010 or 2013.  So, here is how to fix the problem:

1. Create a new blank project.
2. Display the Gantt Chart view with the Entry table applied.
3. Right-click on the Task Name column header and select the Insert Column item on the shortcut menu.
4. In the list of available columns, select the Task Mode column.
5. Right-click on the Task Mode column header and select the Field Settings item on the shortcut menu.
6. In the Field Settings dialog, set the Width value to 9 and then click the OK button.
7. Click File > Info > Organizer.
8. In the Organizer dialog, click the Tables tab.
9. In the list of tables on the right (in the project), select the Entry table.
10. In the middle of the dialog, click the Copy button.
11. When prompted to overwrite the default Entry table, click the Yes button.
12. Click the Close button to close the Organizer dialog.

Repeat steps #2-12 for every table in which you want to include the Task Mode column by default.  Hope this helps.