I empathize with you - this could be a major undertaking. Has he really created a lot of files?
A little planning first would help.
The safest thing would be to do what you suggest, and first just simply copy your entire C drive to an exeternal drive, and then work with this later. Note that you will still have a disorganized mess. But it is the quickest and safest way to handle it. Note that a USB drive will be very slow - although it might be your best option. Other options include inserting another HD if system will handle it or inserting an eSATA card and getting an eSATA drive, which would be much faster for all backups but cost about $100.
In any case, at sometime you should organize the files and you could do this before backing up - if you can take the time.
Can you identify most of them by some set of prefixes (eg. xls, doc ) based on the applications he used to create documents to help you narrow the search to ones he really needs to save? Do you have to go back to the beginning? Can you instead safely say if a document has not been modified in the past two years (or whatever) if can be ignored?
You might start by using Internet Explorer to delete all Temporary Internet Files to get them out of the way - if you have not done so recently.
Consider making My Documents the final resting place for all files - hopefully many of his files are already there. Move all your documents to one file first, then when donr backup that file to an external HD - or burn a CD or DVD if you can. This would probably be much faster than trying to directly backup each file you find.
Then create some kind of file organizaiton plan in My Documents and set up some folders. You can organize the files already in My Documents or leave that for later - just trying to drop files from other locations into the new folders. Hopefully he gave his files descriptive names. Also create a something like a "To be filed" folder to drop in all the files you cannot quickly identify for later organization.
Consider searching on "documents" and "Pictures, music or video" files rather than all files first and transfer all of the files identified there if they are not already in My Documents.
Also take care when moving files that you do not change the location of a folder or file required by a program. For example, make sure you identify where your email program stores emails and don't disrupt that file but make sure it is on your list to copy. You also want to ensure you don't mess with any Windows or other system files.
Since you may have a lot of files to move - you might also try experimenting a little. For instance, open one Windows Explorer to search with and a second Window to paste to. In the second window, open the My Documents file. In the first window, search for all .doc files. When you have the list, see if you can cut - from the Search Window and paste into the Second Explorer window if the My Documents folder or subfolder. Try with one file first to see if it works, and if so, then several at one time, and finally 10 to 20 or maybe more.
Good luck.
After you reformat, you might consider setting up a partition. Computer will assisgn a new drive letter to the second partition just as if you had a second HD. Then put a My Documents file on the second partition - then ALWAYS save there. Move your email file to that drive also. Makes it easy to backup that drive and if you ever have to reformat you can reformat the C drive and still have all your data on the other "drive".