Q: Flashing folder with ?  OS X Mountain Lion i think and not sure when or if backed up. Don't want to lose any files. Which OS X Utilities to choose? Thanks

From what you have described your files are already gone unless you have a backup. The flashing folder with a ? is the Mac way of telling you it can't find system to boot from. This could be a dead drive or a corrupt drive. Either way your files will be gone.

If you haven't already, try the suggestions in this link:

If a flashing question mark appears when you start your Mac - Apple Support

Good that you have a Time Machine backup - hopefully it is up-to-date. If your HD has failed you should be able to restore your data from the TM drive once the failed HD has been replaced.

Startup Issues - Resolve

Startup Issues - Resolve (2)

Startup Issues - Resolve (3)

Try restoring from Time Machine. It is a slow process, so be prepared to wait a long time.