Fishkeeping is an awesome family hobby, especially if you take the time to do things properly (like you currently are!)
My wife and I (married just a week ago
) both love fishkeeping together. And I kept fish with my mom's help since I was 9 up until I left for college- it was a major bonding activity between us. It's a huge learning experience too; your daughter will get tons of hands-on science education, especially in biology and chemistry, from fishkeeping! I ended up going to school for marine science/aquaculture and had a huge leg up in a lot of classes because of my fishkeeping experiences. Maybe (if you haven't already) find some beginning fishkeeping books or online materials and look at them with her- looking at different kinds of fish with my mom and learning about them together is one of my fondest family memories. (Sorry if that was a bit personal, but I can't help but want to encourage fishkeeping as a family hobby for all the good it's done in my life and my family).
Ok, now for the fishkeeping advice! I can't personally recommend and bacterial supplements. Personally I think you're better off fishlessly cycling and taking the time to get familiar with doing water tests and the nitrogen cycle in action. But Tetra Safestart and Dr. Tims are the two that I have heard good things about.
Make sure that the glo-fish you get are in fact the genetically modified kind, and not the kind that are injected with dyes and advertised as glo-fish or painted glassfish. The dye-injected kind are almost certain to keel over within a few months, while the genetically altered kind are otherwise healthy normal fish.
I don't recommend live plants for a first tank. They add an entirely different aspect to consider- it's essentially gardening on top of fishkeeping. It might be too much hassle to be enjoyable for your first tank. If you find, like many of us here, that you really enjoy fishkeeping and want to get more tanks and try something new and exciting, live plants are a good excuse to set up a new tank
I'm going to echo everyone else and recommend a 20 gallon long. It's probably the best tank size for a first fish tank. A 29 gallon is also a good option- it has the same base size as a 20 gallon long but it's taller so there's a few more popular fish that you can potentially keep in it. 29 gallons are also available in kits for $130 (and sometimes on sale for $70) that come with everything you need aside from a stand, decorations and fish.
10 gallon tanks can be hard to maintain good water quality in, because there's not much water so conditions can change rapidly. They're also frustratingly limited in what you can keep in them, so I wouldn't recommend them.
I'm also gonna agree you should pick up a liquid test kit. Not only are they incredibly important for keeping a healthy tank, but they're also a really good chemistry education tool. We actually use them here in the lab I work in for certain applications, since they're cheap and fairly accurate.
I would say 5 or 6 tetras and 5 or 6 danios would work nicely
You could also do a school of fish on the bottom, like kuhli loaches or corydoras catfish. I recommend kuhli loaches as they are quite colorful so they'd fit nicely with the glo-fish.
I wish you the best of luck in your fishkeeping endeavor!