I might just go ahead and drive it down to my local sewing machine repair place. If it needs parts (my dad mentioned it might need a new belt...?) then they might be able to point me in the right direction, or they might even recognize the thing.
Thank you for your responses, now I'm even more determined to learn all I can about my nameless relic. ^_^ I'm still hesitant to fire it up since it's probably been sitting for decades. I'm vaguely aware that sewing machines need to be oiled from time to time, and it seems like it might damage it if I ran it without oiling it first. Which I have absolutely no idea how to do. (Obviously I've been hand-sewing my whole life, this machine thing is completely new to me.)