Thank You Once Again for the help and education.

I very much enjoyed your explanation of how NAS works, Jake. I learned more from it than from all the many articles that I have read to date. The whole concept now makes perfect sense to my brain. (Penetrating this brain is a great compliment to your teaching skills!)

Thank You for the tip about making sure the router can work with Time Machine, Slydude. TP-Lik offers some, but it seems that Time Machine and NAS might be trouble prone no matter what device is used (and it's probably not the fault of Time machine, from what I've learned here). At most, I'd use it as a redundant backup.

I do like using Time Machine. The interface is comfortable and familiar.
Retrieving a file that I destroyed- and I do destroy files- is quicker with Time Machine than with my current off-site program, iDirve. (Which is equally easy, just slower.)

Regarding SuperDuper! and NAS, from what I've read it can be successful if SuperDuper! is backing up to a Disk Image on the network attached drive. I don't know if it is officially supported or even reliable. Perhaps, for fun, I'll try it and will report back what happens. But

My goal to have Time Machine (or I suppose SuperDuper!) plugged in to the router was less clutter on the desk and fewer plugs sticking out of the laptop's ports. Right now, the USB drive (for Time Machine) is plugged into the left port where I can't use a right-angle plug due to the MagSafe adapter plug being in the way. The clone drive is in the Firewire port on the right. No right angle there, either due to the ethernet cord. So my laptop has a rather wide footprint.
But backups are important to me, so clutter a small price.

Was My Project Successful?
I'd say Yes!
I didn't get to connect the Time Machine drive to the router right now, but I learned a lot about NAS, routers, backup applications and related topics. So it was a good experience.

Thank You All again for your help, education and a very interesting series of posts.