There are a lot of options available in pointe shoes now, and if I were a young student I would be mightily confused. And yet relieved, too that there might be a shoe that will fit exactly right, and not be too painful to work in.
If you are a parent reading this, please be aware that there is a considerable financial aspect at stake here. Pointe shoes cannot be purchased to grow into. They must fit like a glove, to be simplistic at the moment, and may not wear out before the student grows out of them. On the other hand, if your child has a high arch, shoes may be broken completely and useless for pointe work, in a matter of a few classes. This situation will improve as the feet strengthen, but must be put up with until then. On the other hand, such students can remove the inner sole, soften what is left of the box with their hands (if necessary) and wear the shoes as soft shoes for regular classes. This saves buying soft shoes, unless they are a requirement, such as for a ballet exam.
At a student's first fitting, a lot of time must be taken. If a fitter or a dance teacher is available, that is a real plus. Not all stores may have experienced fitters.
The individual's foot shape must be examined. The length and tapering of the toes, the width across the metatarsals, the height of the arch, and the depth of the foot must all be fitted correctly. Badly fitting shoes can contribute to sprains and permanent injuries. Good technique can make up for bad fits, but the tolerance of the resulting pain is a waste of the dancer's concentration.
Before you get to the shoes, think about what you might want to use for protection inside the shoe. This will take up space. The variety of gel pads, toe length adaptors, toe tips and all the other things are wonderful, but make sure you have room for them. You may be a fan of a ballerina who has stated "I never put anything in my shoes because I like to feel my feet".... and you should definitely try that after a few years of pointe work - but not now.
The boxes of pointe shoes come in tapered shapes, and square shapes. They must fit so that the foot does not sink into, or slide around inside the box. A longer second toe usually requires a slightly tapered, narrow to medium box, but there are no hard and fast rules. A longer big toe may also feel more comfortable in a tapered box, but every shape of shoe must be tried on.
Take a pair of tights with you, to put over your foot and try the shoes on. For your first fitting, don't wear the tights, as the fitter may ask to see your toes, if there is a problem getting a fit. Just in case.
You can check the vamp needed by rising up to 3/4 pointe, and seeing if the shoe break is wear your metatarsal joints are. Too high a vamp will impede the foot movement, and too low a vamp will not provide support.
The stiffness of the shank will be determined by the arch height and ankle flexibility. You need to be able to get up onto pointe fully, so that you are not working leaning into the back of the box. So the shank must give support but not present so much resistance that you can't work properly. Most shoes will break in, and keep breaking in until suddenly they are worn out! That's the life of a pointe shoe..... Gaynor Minden's are different, and that site explains exactly how. They don't break in, so you need to buy exactly what you want to work in. I have never worn them, so please do your research for exactly the right fit with those shoes.
When you are up on pointe, there should be about 1/4 inch of fabric at your heel. If there is none, the shoe is too short. If there is more, the shoe is too long. Also, if you do a demi-plie, and your toes are mashed into the box, hurting, the shoe is too short, too narrow, or both.
The vamp should not gape or wrinkle - neither should the sides. There should be equal pressure from the shoe all over the foot.
I've tried to keep these articles fairly short - but like your first few fittings - time, patience and detail is needed.
Here are a couple of wonderful references I have found ;
http://www.the-perfect-pointe.com/HavingAFit.html is a detailed article written by a pointe shoe fitter
http://www.the-perfect-pointe.com/list2.html is a graphic table of pointe shoe specifications. It is an excellent guide to start with before you shop.