Hi, angel_eyes! Welcome to the forum! I started my bike quest at my local bike shop. I guess I could've bought it at the department stores, but all the info I got mentioned to go to LBS. The first one I went to was okay, but not necessarily hip to service, and the other one that's closest to me wasn't too great either. In any case, just test some out before you buy. Buy from the LBS that you feel most comfortable with, too. I finally found one that I like, and they give me lots of good info--even if they're farther.
Okay, I'm pretty short, so I ended up with a smaller frame, so make sure you get a bike that fits you...you should feel comfortable riding it.
When I was a kid, the only bikes I had were too big for me, so I was eventually falling off of them quite a bit. I really love my Trek 820. You might do a search in the Women's forum for bikes made for women...a few posted about Terry bikes, but I didn't have the chance to look at those yet.
Good advice about getting used to your bike first, before putting your daughter in it. It's always good to break yourself in on the bike, so you know how it works. It took me a little while to get used to all the neat gizmos on the bike. As kids, we only had the pedal to use as brakes, and now I'm using brakes with my hands (okay, not with my bare hands...)! Go figure!
Hey, I'm still learning, too! This place has lots of good information and tips on where to find them. It's also great fun, and quite addicting.
Good luck with your quest!