After much deliberation, I walked down to Webs today and got their drop spindle starter kit - a Louet spindle, a book on spinning, and half a pound of wool to spin. And I've started spinning my first skein! Yay!
It's a bit lumpy, and I keep going from long sections of thick yarn to long sections of thin yarn, but I think I'm catching on to how you do it. Drafting is taking some getting used to, but even if I can't actually do it properly right now, I think I understand how it's supposed to be done which means I just need to teach my fingers how to do it. I think I'm over-twisting most of it, but I think for my first skein, it's not too bad. I seem to have figured out how to join pretty well and the joins are strong, but they're really fuzzy.
This is so exciting! Once I actually knit something with yarn I've spun, I'm just going to go around showing everyone I know!