Thank you, thank you, thank you!
I would suggest very strongly that you get tutoring at the start, either in person or over the the internet. Chinese tones are not optional as they radically alter meaning (from 'horse' to 'mother' to 'hemp') and they are very hard to pick up without correction.
Yeah, the more I look into it, the more I realize this is not a DIY/muddle through on your own kind of subject.
If you don't have a background in Chinese, I would suggest you sign up for a class. For example, there's a teacher (last name Hong) who homeschooled her kids who offers classes online on outschool and currclick. That might fit the bill. This would solve the issue of getting a tutor.
As to whether to use My First Chinese Readers, I actually would suggest you look at My First Chinese Words series from Better Chinese instead first. I know they list it as pre-K/K, but it is fine for a 7 year old. There are quite a few apps that you can get that demonstrate writing Chinese characters and the correct stroke order. You can print out Chinese "guideline" paper. I would suggest using the rice template here. It will help with figuring out how to position where to start and finish a stroke. Though if you signed up for a class, you wouldn't have to get a curricula...the instructor will have their own selection.
I looked up Connie Hong's class, and we are just in time for the beginning of this semester. I'm really leaning towards doing this. It's more expensive (and rightly so), but I think it will be worth it. Plus, her first class is only 6 weeks. I think that will be enough to give my DD a taste of the language, learn how to write some characters, and see if she wants to learn more.
Yes - definitely leaning toward more multi-purpose, not at all expensive, sturdy brush pens/markers.