My mom and I used to watch Dr. Who together! I hardly remember it, I was so young, I'm rather amazed actually that I liked it so much at such a young age, I must have been 7-10 when we watched it. I don't remember it hardly at all anymore.
The most economical, flat-laying stitch is seed stitch, because it doesn't contract width-wise like ribbing or height-wise like garter stitch. Don't know if it would look Dr. Who-ish, but it would look cool. I think it would be more tedious though, personally, than garter. Any stitch you do for 10 feet is going to be tedious. I say just do the stitch that is easiest on the hands and that you can do while watching TV or other things, which would be garter stitch. If you don't know how to knit without looking, this could be the perfect opportunity to learn!
I actually love to have this kind of project on the needles, in tandem with any other project, because I like to have a mindless project that I can do while talking on the phone (with my headset) or in the company of friends, without looking.