Which set of files I need to backup or store in a version control system to completely recover project settings and related debug settings?

The files you need to store in a version control system:

• .project and .cproject - contains the list of files and the build tool settings.
• .ttf - targets the needing target tasks for flash programming (ColdFire V2 and Kinetis IAR JLink)
• .launch - required for the debugger launch configuration
• rseHostSettingsCache.xml- contains the cached RSE settings. You need this to have the RSE settings imported.
• *.c/*.h/etc source files and linker file, if not using Processor Expert
• If you are using Processor Expert - ProcessorExpert.pe (contains all the settings), events.c/h, and the ProcessorExpert.c with user modifications

Any generated folders (like PE Generated_Code, PE Documentation or the folder where the object/make files are placed (usually named by the CPU name) can be stripped off to reduce file size.

You can also export/store the workspace settings, like editor/VCS settings/etc, by selecting, File > Export > Preferences from the IDE menu bar.