Hi David,
You are right, this is controlled by the process configuration. Assuming you have rights to edit the process configuration, from the eclipse client, right click > Open  the project area where you want to implement this and navigate to the Process Configuration Source tab.
Under <project-configuration> --> <data> --> <configuration-data> you will see all the work item type ids are listed under <type category...> tag.
By default, the first one is Defect if it exists. Suppose you want to choose Task as the default work item type instead of the Defect, you can cut and paste the whole <type category> tag (till the </type> end tag) and put it as the first one under the <configuration-data> tag. Save the process template and try creating the work item from the "Welcome to Work Items" page.