CCMs are bad. Good hockey skates, terrible figure skates.
And yes, the rental skates aren't good at all at most rinks. They're usually bent, missing insoles, not very sharp, etc.
Jackson and Riedell skates are pretty much the most common real (as in meant for more than occasional use) figure skates in America, both being US based companies. As far as the boots you listed, they're probably good for her level. Your best bet would be, look for used boots. Just make sure they're still reasonably stiff (as in, the sides don't bend in when you push them towards eachother) and the soles aren't falling off the boot.
One thing with skates, as far as sizing them, they're much different than shoes. You want the big toe to touch the skate, but not bend the toe, and then when laced up, you should only be able to fit one or two fingers between her heel and the back of the skate. Figure skates for me run a bit more true to shoe size, but in hockey skates, I wear size 9 or 10 shoes, but I wear size 7 hockey skates. My figure skates I think have been about a 9, and most shoes I'm a 10. One thing that's a problem with skates is a lot don't accommodate wide feet without ordering a wide version of the skate. Some brands are better than others, ie, Jackson is notorious for running wider, but yeah. So with shoes, some people just wear too big shoes all their lives because they're substituting length for width. Like Vans for example, are a wider running shoe than Converse, Vans I can wear 9.5, Converse I have to wear 10 or even 10.5. So that's the big issue, when you wear too small, your feet are cramped, and thus hurt (though in my experience, my feet hurt less wearing too small than too big) but if you wear too big, to keep your feet from sliding about in the skates too much, you tend to tighten the laces ridiculously tight to compensate, and then the tight laces push down on the foot, and give pain especially in the ball of the foot/middle of the foot. What happens if your skates are really too loose (or if they're very worn/badly made and floppy) when you step on the ice, the blades are like / \ instead of | | , and with the blades like / \ it's pretty much impossible to skate. That, and if they're too loose, that's when you get complains of hurt ankles and stuff, as the boots aren't supporting the ankles because they're too big.
But, the difference between your own skates and rentals is pretty night and day. Your own skates, you can sometimes heat form them to the feet, or if they're too tight in a certain spot, punch them out to fit you better. Also, the blades, the bottom of skate blades is actually a U shape, and the radius of it goes from, say, 1/4 inch, to 1 inch, what that means is if you drew a circle based off the skate's radius, if you got 1/4, it'd be a 1/4 inch circle, but with a deeper hollow on the bottom of the skate, you get more bite, or with a shallower hollow, you get more glide, etc, so there's that.
So yeah, I mean, you can get some good deals sometimes on skates. Generally you'd be spending a tad under a hundred new for a pair of figure skates, but the drop out rate for figure skating is higher at those ages, so there's a bigger market for used skates for your daughter (compared to if you're a 21 year old male like myself,) just sizing is pretty much the most important part of selecting a skate. You really wanna get her skating in something decent, though, so that way there she can get a fair view of skating, because if she skates in wrong size or really broken down boots, she'll probably hate it and quit. Also, if you wanna skate, and have the time to do it, it's wonderful exercise, it burns as many calories as running does per hour. So it'd be a good way to spend time with your daughter and get some exercise.