How to change which modules are auto-applied in Darktable?

Automatic presets would do that, see the section "Module presets" in Darktable's user manual. Note that you need Darktable version > 1.4 for this to work sensibly with lens correction. In earlier versions the lens correction did not adapt correctly to the image parameters.

Relevant section from the manual:

A module has an expander bar . Clicking on the name of the module expands the module's GUI with all parameters.

In its default setting darktable will only expand one GUI at a time. If you click the expander bar of another module, the previous GUI gets collapsed. If you want to see more than one GUI expanded, you may expand further modules with shift-click – all previously expanded GUIs remain opened. The expander bar behavior on click and shift-click, respectively, is controlled by a preference setting in gui options (see Section 8.1, “GUI options”).

Expanding a module does not activate it. You need to click the icon to turn a module on or off.

Icon accesses the module's available presets or creates a new preset from your current settings (see Section 3.2.3, “Module presets”).