My eldest asked me to teach her to read when she was six. I felt the most important thing was that she found the books engaging, so she sampled various ones before choosing. Buying a whole set of books can be risky. You may feel stuck with them because you have invested money in them, and carry on too long even after discovering they aren't right for your child. I suggest trying different ones to see what she likes best.
You don't necessarily need special "reading books". Kids have different ways they like to learn to read. Some will just pick up reading spontaneously by looking over your shoulder as you read to them - does your daughter like to do that? My younger child didn't like formal instruction and just picked it up for herself through computer games, emailing relatives and friends, and looking at familiar books she had heard before.
Also, though your daughter is showing interest in learning to read now, be prepared for the possibility that this interest may come and go. My eldest initially showed some interest in reading at four and I'm sorry to say that I jumped on it too enthusiastically, which put her off altogether for several years! But without school in the picture, there is no hurry, so they can learn to read whenever they are ready.
Once they get stuck in, they tend to learn really fast. By the time they are ten you wouldn't be able to tell the difference between a child who had learned to read at four and one who'd started at seven. Later readers' education isn't harmed, because they can access it in other ways: discussion, being read to, watching documentaries, or hand-on learning. (That isn't true for schoolchildren. Schools push reading hard, so a 7yo at school who isn't yet reading will feel she's a failure, which has long-term consequences. Plus, as children get older, schools increasingly deliver the curriculum via reading and assess it via written work. In the one-size-fits-all school system, kids DO miss out if they can't read. So the clock is ticking for nonreading schoolchildren.)
So my advice would be to pay attention to what your child wants and enjoy the flexibility of home education for her to learn to read whenever and however suits her best!