I'll chime in. I am a skater and a mom of 2 skaters. I grew up skating.
When I was a girl, another girl came to the rink. She had several years of formal dance school under her belt. She was spinning in 6 months and did an axel at a year. Ballet is extremely good for skaters. Yes, there are some moves that are done a little differently. Dancers are going to pick up skating quickly. If you want so see a high level ballerina doing skating, Youtube "Bellita". She was light years ahead of her time.
Basic skills are skating across the ice, simple turns of directions, backwards, stopping. Freestyle is the beginning of one foot spins and turning jumps in the air. Skating is balance, and each move builds on the other. At my rink, they offer "group" classes up to Freestyle 6. This is camel spins, lutz jumps, some girls doing an axel. Group classes are a great, inexpensive way to get fairly far into skating.
The beauty of group classes is there is a different coach each session. You and your daughter get to preview these coaches. You can pick a coach right now, or you can wait. There is no problem in switching a coach, just that you have to tell the old coach that you are switching. Don't start with a new coach and then never tell the old coach he/she is through. Or, leave a balance due with the old coach. Coaches are likely better friends with each other, then they will be with you. Coaches have worked together for years sometimes, attend conferences together. You and your daughter are another parent/child that passes through their rink door. Word will get around, if you are difficult parent. Coaches sometimes gravitate towards certain levels of skaters, and will "hand off" when the skater gets too high for them. Sometimes, the coach just doesn't want the challenge of the pressure put on them by the parents of top skaters, so they prefer to teach intermediate students. Skating moves can take years to master. If your daughter doesn't get a move quickly, it is not reason to abruptly change coaches. If so, I'd have gone through every coach at all the rinks in town! The most important thing is that your daughter can understand the coach and the coach can tune into what she is doing wrong and give the right correction. Learning something wrong is the worst thing a skater can do because it takes a trillion times more to unlearn the bad habit. That's going to cause your daughter frustration and you alot of lesson money. A young girl can do a single jump completely wrong because she's a twig, but she will not be able to do a double jump with wrong technique a year later when she grows.
The second most important thing to a coach is that she is supportive. Some kids need a tough coach, because they are lazy or wimp out. It takes courage to skate. Other kids need a super encouraging coach because they lack self-confidence or need a softer approach. No kid needs a mentally abusive coach. Keep your eyes and ears open, as to what the coach says and how she says it. Coaches have to give criticism. This is why mom & dads are not good coaches. She needs mom & dad for unconditional love. After videotaping and critiquing each element of my adult Bronze test, and going over stuff that needed my improvement over the rest of July . . . . my coach told me "good job" and it made my 45 year old heart.
I think many skaters do the group lessons through learning the one-foot spins and single jumps (i.e. ISI Freestyle 6). By the time they are in ISI 5/6 Freestyle, alot are doing both private and group lessons. Some, if they've done the mini-competitions, will also have a private coach at doing three turns. That's the best, if your wallet allows it. At the point of flying spins and axels, then it's all private coaching and usually only on freestyle ice practices where only figure skaters are allowed. Speaking of practice, she will also need to practice skating three to four times a week. It's better to go three, one hour sessions a week, then one, three hour session a week.
At the end of each group lesson is a casual test where the teacher tests your daughter. Like dance, they will not move a girl up if they think she's not ready. They are not going to risk your daughter's safety. Also, your local rink likely has small competitions where even the basic skills people can put together a program. Most will hire a coach to help them choreograph a simple routine within the skater's level. There are rules, like time limits and elements that must be in the program. The coach has the know-how. Then, that coach will work with the skater to master the program before the competition. You can be upfront with the coach, tell her that you don't want to commit to a long time relationship with a coach at this point in your skater learning the sport, and are just asking for help with this one competition. You don't have to be a USFSA club member to do these competitions. And, you don't have to have a fancy dress either. A plainer skating dress is just fine. And, you don't even have to do these mini-competitions either. It's all up to you.
The USFSA/Club member is to test in a panel of 3 graded judges. They are very picky that each move is done correctly. People doing their "Pre-preliminary moves in the field" and "pre-preliminary freestyle" are on Youtube to give you an idea of the entry-level of USFSA. If you or a coach thinks your daughter will be at pre-preliminary soon, then join the club. Otherwise, save your money for ice time. There are alot of USFSA levels; pre preliminary, preliminary, pre juvenile, juvenile, etc. Here is a decent discussion of the levels,
http://www.iceskatesnblades.com/USFSA___ISI_Test_Levels.html Meanwhile, I'm sure that those in the club will let you borrow the Skating magazine. I really love it when it comes in the mail.
Skating is the ultimate sport. It combines strength, balance, grace, aerobic, coordination and artistry. It is also very hard mentally and physically. In dance, you don't do a solo in your first year. In skating, they push for solo early on. USFSA testing is all done solo. That teaches self-reliance. In the end, you can't really blame anyone but yourself if you did poorly. Your whole team helps you arrive at the competition (mom, dad, coach), but it's all on your shoulders when you step on the ice. That's alot of pressure. If you can survive figure skating, you can survive any profession. And so, there are alot of girls skating. Alot are good. You have to go into this expecting her to learn more life skills and becoming extremely fit and healthy. Few make it to the Olympics, just like in dance where few are going to become professional dancers.
If she loves skating, let her do it. When I was a kid and even now, I'm miserable person if I can't skate. It's an adrenaline rush to sail across the ice. Spinning and jumping are still highs for me, and I'm 45 years old. My parents never had to drag me to the rink. I had to drag them to get into the car.
There are ways to save money, and until she's Olympic level it does not have to be super expensive. I take a half hour private lesson once every few weeks. Group lessons usually have coupons for public skating. Freestyle can be purchased in bulk, say 10 sessions for $100. The super avid skaters buy unlimited freestyle sessions for a few hundred a month. But, she's not at that level . . . yet.