Briefly read about the speakers and the headphones.
I work with Music (Audio) all day and 90% of the time I aim to get the perfect audio sound. That is ultimately what I do for a living. Getting music to as near perfect as possible. With the help of special equipment, software and spectrum analyzers I still need the correct audio devices.
Something to take into consideration when buying Speakers or headsets is that they are speakers and not monitors (Different type of speaker). If you aim for the "perfect sound" then look at Studio Monitor Speakers (Desktop). They are extremely pricey since they are NOT SPEAKERS but MONITORS and designed to give clarity and play back the audio as the original artist intended it to be. When using Monitors all settings should be at flat and pre-amp settings should not exceed 50%. In general, they are not LOUD, but the quality and purity of sound is incomparable.
Headphones, check that the inner ear dome (Inside of the headphone) is far away enough to not rub against theear. Prolonged use with these rubbing results into painful ears (The round part from your cheek side toward your ear) Not sure what that Lobe is called. Would seriously suggest testing the headphones with your daughter first. Else she will not have much enjoyment with her new headphones. Place it on your head and move it around (Not pushing and pulling just slightly in all 4 directions. You will feel if it catches that little lobe. If it does, look for something else possibly with a thicker padding or a domed Speaker (Or Monitor, budget dependent). Domed inwards to give the ear more "head room"
Speakers, if what you are aiming for. Desktop you can get JBL Professional 308P MKii Monitors. Remember they sell per each, so you need to buy two. Floor standing, then maybe something like Klipsch R-28PF (a set).
Keep in mind this is High end Monitor speakers, so they come at a price. But if you want to do it properly this would be the way I go.