I wear a 36D. My go-to everyday bra is Fruit of the Loom extreme comfort bra. Stretchy cotton, no padding, adjustable, underwire. It is both comfortable and supportive if she can forgive the underwire. I get a perfect fit with these.
https://www.amazon.com/Fruit-Loom-Extreme-Comfort-White/d...
I don't have Genie bra but I have similar style sleep/lounge bras which are *very* comfy, but not terribly supportive. I wear them at home. She would probably like them, but they won't do for being active.
How does she feel about sports bras? Most of those come without padding or wires, but depending on what kind of clothing she likes to wear, you can have a uniboob look or a strap/material exposure issue.
Tips: Make sure she has a proper measurement. Most women wear the wrong bra size (usually a too-small cup) because they have been improperly measured. Even most fitters in lingerie stores/departments tend to take measurements incorrectly. (Check your own too!)
Cup size is properly measured while bending over parallel to the floor, not when standing up straight.
http://sameatschildren.tumblr.com/post/45962915522/do-it-...
Also, make sure she knows how to adjust her breast tissue in the cups after the bra is on. The underwire or band should touch the underside base of the breast, no gap. Her size uses the scoop & swoop method:
http://bustyresources.wikia.com/wiki/Scoop_and_swoop
Properly fitting (non-sport) bra checklist:
1 - The band does not ride up. It is parallel to the floor.
2 - The center gusset lays flat against the breastbone.
3 - The straps do not dig in nor slip off the shoulders.
4 - Breast tissue does not squeeze out the sides or bulge over the top of the cup.
5 - The top of the cups rest gently on the breast. It does not press into it, nor leave a gap.
Well, I think I fulfilled my quota of talking about boobs on the internet. Good luck to you and your daughter!