I have met many parents in the ice rink who look for the first figure skating blades for their daughters.
Here my two cents to share:
Skating boots need to be comfortable, and at the same time provide enough support to the ankle. For non-skater, you can start with a cheaper and softer version. For more advanced level, you probably need the boots to be harder and supportive. There are different made of blades themselves also. Some blades are harder and last longer. However, as the child outgrow skating blades very fast, it is probably not the biggest consideration unless, the child is a really good skater.
Riedell and Jackson are two popular brand names that fits a beginners need a budget.
Riedell 10: My daughter’s 7 year old friend has it. She is a really good skater and I feel she should get a better version than this. However, she seems to be performing really well still in this verion:


Jackson Softec: This is a more comfortable verion fo Jackson:


Jackson Mystique: My daughter is learning spinning and jumping. This more expensive version is made with harder leather and provide more support for her.

American Athletic: This is a cheap brand name I can find. I have never tried it. But it should fit the beginner’s need with low budget.

There are what is called “convertible” skate blades that can adjust for feet size. Those one never fit the children’s feet very well so I don’t suggest anyone to buy it.