So, I thought of a couple of things I should have included in the original post. I'm going to include them in the original post, too, so it's all in one place; but for those of you who've already read it, I'm going to write them here first, so you don't have to dig through the whole other post looking for the updates.
ROPES
It turns out, my PVC jump rope is 9 feet long. All of them are at the sports stores and stuff, unless they're for kids. Don't worry about this. They're all adjustable, too. There are various sites on the Internet that will give you advice on correct rope length. I don't think I've discovered anything particularly useful on this topic. I haven't adjusted my 9 foot rope; neither has Rth adjusted his, and he's about 5 inches taller than I.
SHOES
You really must wear shoes. Mine are cross-trainers. I'm betting anything you've got from court shoes, to cross trainers, to something made for aerobics, to running shoes will be great. Just make sure they're properly supportive shoes for moving around for you.
SUPPORTIVE WEAR
I am the kind of woman who believes in a good sports bra, regardless of your chest size. If you're the kind of woman who doesn't believe that, or if you're a dude and just don't care, that's cool; you can just skip the rest of this paragraph. I highly recommend
Shock Absorber sports bras. They're sold through many online stores, many of them not in the UK so don't worry about the shipping and all that. I have some smaller friends who really like their options in the A and B cup range. I have been using them as a DD and D cupped woman and really like, in particular, the Support Level 3 Anti Bounce Sports Bra Top (style B518, second from the bottom in the Support Level 3 slider). I'm surprised at how much I just completely don't bounce around in this bra, considering it is not the highest level of support.
Also, whatever else you do on that site, you must click on the "Bounce-ometer" button on the main page and watch the animation. It is hilarious.
As far as I can tell, none of the guys I know who are regularly jumping rope are wearing anything special to do this. I'd be interested in hearing from y'all if you are; for science, of course.