Just my thoughts on the style and fashion of the three skating dresses----
The First one, the red and multi-colored, streaked strapless dress, is not age-appropriate for a 13 year old skater, a beginner skater, or some combination thereof. It's not good even for a competition dress on a girl that young. It is styled for a much older teen skater, or an adult skater of smaller stature, IMO. As a judge, if I saw that dress on a little girl, I would be embarrassed for both her and me. Maybe I'm just not up with the latest, hottest looking styles, but that's just me.
The Second one, the pink dress is the best choice ! It is pretty, with somewhat of a " Broadway " style, and that would add some spark to the skater's presence, even if she is a beginner skater. I think the pink dress would make a good competition dress, especially if stones or sequins were to be added.
The blue dress, the Third one, is nice, too. Blue has a bit more mature look to it, but would be fine for a 13 year old skater and/or a beginner skater. The blue would be a nice practice dress as is, or could be upgraded to a competition dress with some additional add-ons and reworking of the accessories.
The Fourth one, the one shown later in this thread, would be a very pretty and fashionable practice dress. The turq color is bold, but the dress is not overpowering. A beginner skater could be proud to wear that dress, even if she is learning and prone to mess up or fall quite a bit. The dress speaks confidence nevertheless.
Probably your best advice is to take a consensus of what everyone says, and decide from there what to do and what to have your young skater wear.