You should be able to get your data back. Having the drive connected via your USB is fine.
When you run Recover My Files (download from
www.recovermyfiles.com) the first search you should try is a "Fast Format Recover".
In the drive selection window, you need to search the "physical drive". A physical drive is an actual piece of hardware (i.e. a hard drive) installed in your computer - as apposed to a "logical drive" (i.e. a drive letter - you can have more than one logical drive on a physical drive).
Searching the physical drive allows Recover My Files to treat the hard drive as one big chunk of raw data, and gives it the best chance to find all files.
A Fast Format Recover is Fast (should take less than 40 minutes) which is why you should try this first. It does not always work, so depending on the results, you may like to follow this up with a Complete Format Recover. Again, search the physical drive, and search only for the default selected file types.
At the end of both the searches, Recover My Files will try to rebuild the old file system and display the results in Folder View of the results screen. You should be able to click on the files found and preview their content in the results screen. If you can see your files, then you can purchase a product activation key and save the files back to your C: drive. Once you are sure you have all your important files (perhaps you should also make a backup of the backup), then in you case it is probably best to reformat the drive and start over.