Let's look at getting proper equipment for racing, including skis, boots poles and protection etc.
There are many gear guides published, like Ski Racing's gear guide, which you should certainly read, but they, while giving you an overall idea, will not get into the details of choosing ski race equipment.
When you buy race gear for your racer, you have to balance a few conflicting needs, saving money vs quality equipment, "buying big so they can grow into it" vs a good fit etc. It is ok to get skis that are a little big, but it is not ok to get boots and helmets that are a little big. It is also ok to get second-hand skis, but only lightly used boots (as the liners pack in with time).
As a rule of thumb, invest in boots more than skis, so rather than getting older boots to afford a new pair of skis, get older skis and thus afford better-fitted boots etc.
The boots are the most important piece of equipment and, for racing, you'll want stiffer race boots. For juniors, these start around 60 flex and go up from there.
Race boots are stiffer than regular ski boots, with a narrower profile and thinner padding, to afford better control and feel, much like a race car's low profile tires. They also offer more adjustment options.
For U16 and up, generally 70 flex would be minimal, 90-110 is average (130 for adults) and there is the occasional racer in 150s or even higher, at the WC level. Don't go too stiff too fast: ask for a coach's feedback - it is quite noticeable when you're in softer boots than your skill level.
Flex is also related to your weight and body build, not just an absolute number, so there are many criteria to use.
Go to a reputable shop and ask for an opinion. Based on your feet, some makes and models may be more appropriate than those sporting your favourite colours - so don't go there looking for a specific brand (unless you really know what you're doing).
One finger is a good race fit while two fingers is a generous recreational fit. Anything more than two fingers means you need different boots! If you want to be more precise, use wooden dowels: 3/4 inch and one inch instead of the fingers.
Make sure the boots are "race fit", i.e. with the shell fitting method, there is room for just one finger behind the heel. Two fingers is too much for racing, as you'll be sloshing around in the boots and have no control over the skis.
"Oh, he/she'll grow into it next season"... sounds reasonable, but you're doing them a big disservice: in large boots, you can't control the skis very well and they are forced to cheat by turning with the hips - doomed to learn and ski with bad technique.
It's a much better idea to buy good fitting second hand boots instead.
If you want to get serious, these are the best resources on boot fitting:
For U12 and up, especially as the technique improves, the boot fit becomes important and they will need to be aligned and canted properly, with the help of a knowledgeable coach and good boot fitter.
Likewise, depending on the shape of the foot, custom footbeds may become important as well. One important issue here is to get a boot tech with race experience: footbeds must be fitted to the small room available inside a race boot and must not restrict the movements of the foot inside the boot. It can get pretty tricky and technical.
Equipment and tuning guides for racers and parents:
Full battle gear. Skis a little sharper.
Boots fitted and aligned. Skis fast and razor-sharp.
Alpine racing skis are stiffer and harder to ski well than recreational skis. They are all narrow because they're made for ice.
You need to get an appropriate race ski, even at the smaller ages: recreational skis are made for a variety of snow conditions and ability levels and cannot put up with training and racing on hard snow and ice.
Generally, up to U14 we use "junior" race skis while for U16 and up, depending on size and ability, we'll have to choose among 3 different levels of "race" skis - most manufacturers have about 3 ranges of race skis between masters (more friendly) and FIS (more performant). Most also have a race room version, hard to get, reserved for top athletes.
Good clubs will have a few different skis for athletes to try. Failing that, demo days are the thing to go to, although they don't always bring the race equipment. Testing, especially at the higher levels, is how you'll find the fastest ski for you.
The rule of thumb is that, unless you are looking at racing at the highest levels and especially at the younger ages, you don't really need to get new equipment. Reasonably used skis are much cheaper and you can swap them much easier when you find something that suits better.
Save your moneys for good custom boots and training... you'll need both!
The general characteristics that we use to choose race skis are:
For Slalom, the radius of the ski varies between maybe 8m for juniors to 11m for some masters skis, to around 13m for FIS. The smaller the more maneuverable and easy to ski. Don't get an "all mountain" 16m ski and expect it to be ok in gates: it won't be!
Slalom skis are also shorter and more manoeuvrable... often lovingly referred to as "disco sticks".
GS skis, because of the recent changes in radius and sizes, come in many varieties: from 14m junior skis to 17m cheaters, to 21-25m masters to 30m FIS compliant. The differences between these are not just radius, but also stiffness. Choose based on your current ski ability: if you're an experienced racer, a 23m can be a lot of fun, although an 18-19m can provide a lot of fun on all sorts of sets. However, always make sure to read the guidelines and rules for the specific racing organization you'll join.
You'll see racers on 30m skis carve down a course where you can barely make the turns with your "masters" 17m skis and that's normal, it's the skill level: they have many years of training in these conditions on you.
FIS racers do not have many options, they are constrained by the very specific rules set out by the FIS. Local leagues and especially at the lower age groups have more relaxed rules.
Speed skis are more specialized and, while there are the "standard" dimensions that FIS mandates, you need specific advice when selecting those.
For juniors, choosing skis is simpler, as there's just one category of junior race skis, which should be matched to the racer's body build and current skill level. Talk to the coach or see these general guides to choose for the appropriate age: U10 | U12 - U14 | U16 - U18.
For U16 and up or adults, at the lower end, a "masters" ski can be slightly wider than a full on WC race ski and thus usable in more conditions and a little more soft and friendly - although that will sacrifice some grip on ice. Some slight tip rocker is now quite common as well.
While more friendly, these skis will not hold up well in serious racing conditions, on ice and ruts and high speed as well as the power developed by top skiers. However - It is a very good idea to have one set of these as you start racing and learning to ski well - with the premise that it would make it easier to learn technique and ski courses until you become one of these top skiers.
The DIN range on master's bindings is usually appropriate, but something to take into account. Keep in mind that it is a good idea to have your specific DIN fall somewhere in the middle of the binding's DIN range as opposed to right at either end.
It is much, much easier to learn technique on a more friendly ski than on full on stiff FIS race skis. There aren't many good reasons to not start with the more friendly skis, the only one that comes to mind is weight: if you're big and bend the skis just by standing on them, in that case maybe start with the stiffer ski.
Towards the other end of the spectrum, there is the FIS race ski. These are the stiffest and most unfriendly boards, made solely to put up with the speed and power of top racers. One thing that some do with success is to get well used FIS race skis, which have been softened by say 60-100 days on snow already and thus easier to ski on. Another way to mitigate this is to get a pair from a different category, being quite common for older or beginning male masters racers to use a women's version.
FIS skis often come in different flexes, to further match the skier's body and ability. Some like Fischer simply mark them as "stiff" or "medium" while others like Atomic give out actual flex numbers like 35/25 or such.
One thing to also keep in mind is that when you buy a FIS race ski, this is not quite what is raced on the WC circuit. At the highest levels, athletes have access to a different build of the same ski, called the race room ski.
Again - one thing to keep an eye on if you get used FIS skis is the DIN range of the bindings, which may be too high for you. Always know your DIN and check. It should ideally be in the middle of the range of the binding you're looking at.
Aside from the two that we looked at above, some manufacturers have then a range of middle race skis (marked accordingly and generally for GS). For instance, Fischer cca 2015 had the "RC", the "Masters GS" and the "FIS GS".
Once you've considered all the criteria above, the length is fairly easy to choose. For Slalom, between chin to eye height and for GS, between forehead to 10cm taller.
For racing certain leagues, the respective rules may prescribe minimum and maximum lengths and radiuses, make sure you check.
As the skill level improves, more elements become important in choosing skis and we need to test as many of these we can: we will need to put in place a testing plan.
Skis and boots are very specialized tools and there are major differences between different manufacturers. With boots, it is easier, in the sense that a good boot fitter will tell you the models you should look at, based on your foot and body configuration. Do not go for colour or buy Head just because John likes them. They'll fit and react differently for you!
With skis, it is more nuanced. Do NOT expect to remain on the first pair of race skis you buy. Especially as the skill and level of competition go up, you should try as many models as possible, on a course, in controlled conditions. You may be faster on a ski that seems harder to ski - that's actually quite common.
If you want to be fast, then go for the fastest ski for you! See more ideas in Ski behaviour and testing.
The same goes for juniors. At a certain level, say strong U14 and up, a good club will have a few pairs of different race skis for them to try and coaches should setup equipment testing sessions, to help select the right kind of ski for each athlete. These should be on a course, in controlled conditions.
Many clubs do not and it is then up to the parent to do something about it…
Race poles tend to be different for GS and speed events, curved a little (to be more aerodynamic as the speeds increase) and with an inverted basket. Don't ski GS with a slalom pole, as you'll lose the baskets from the contact with the gate, as you get better and you get close enough.
The SG and DH poles, when you get to counting hundreds of a second, can be moulded to your body. Ask at the local racing shops about this service.
As a hard-ear helmet is mandatory for racing, getting one is the easy part. If you do slalom, you'll need full battle gear, including shin guards, hand guards and chin guard. For GS, it's usually good to have some foam padding (GS race suits come with padding) and a back protector. Arm guards are good to have as you get more aggressive and start smacking the gates out of the way.
Hard-ear helmets are not really required for Slalom, according to most rules now, but are highly recommended. Especially for beginners (i.e. anyone racing anything lower than FIS) - they tend to be hit by gates all over the place and to fall awkwardly.
Here are some of the components. Most come in adult and junior sizes, so choose carefully:
Here are some more resources and articles on buying gear: