I started doing 5k's in August after 8 weeks or so of training slowly. I will 100% say, get a good sports bra. I mean one that's 40 bucks and I like the moving comfort brand, because even though we'll lose weight and need a smaller one in a few months, it was totally worth the investment for me last month when I realized that my dingy sports bra was really causing most of the jiggle in the upper body. I felt if my boobs weren't secure that the rest of my stomach area was even less secure.
Now no more uniboob or jiggle! It is so hard to run when your boobs are everywhere. I know you mean your stomach too, so I also say just get a loose fitting shirt and that's what made me feel less self conscious at first.
Once I got my groove going though, (and my awesome sports bra), I feel I am moving as a unit!
I will also say, I do run on a treadmill too but I also run outside because in the realistic i'm running a 5k, I don't run at a constant pace for the whole race. It's nice to start slow and then speed up and run slow when you just feel tired and etc. Soooo find yourself a school track that you can invade and try running on there! At least so you can kind of find your groove.
Good luck, you'll be a cohesive unit soon enough.