Here's complete details on equipment requirements for all ages.
The time to look for equipment is really october - november, when there are last year's models on sale and ski swaps in full swing.
At this age, the kids have ony one "do it all" ski, set at 1 degree base bevel and 2 degrees side bevel. Save your moneys, get a second hand pair at a ski swap... invest in tuning tools instead!
The ski should be a junior race ski with a short radius, with a length between the chin and nose and flex suitable.
Boots fitted properly - I know you feel like getting large boots to last two years, but don't exaggerate! Read more about Ski Boot Fitting.
In terms of safety, a hard-ear helmet is mandatory for racing. Shinguards are good, since they may spend some time in stubbies - will save a few pairs of pants and maybe their knees and encourage them to get close and personal to the stubies.
Pay attention - there are adult and junior size shinguards - get the right size.
When you choose the helmet (or all equipment for that matter), do allow some room for growth, but not too much or it will loose its safety properties.
Change their ski socks at lunch. Ski socks are much better than regular socks at keeping the foot dry and thus warm.
See more details at the bottom and Ski equipment and tuning for U10.
While the U12 are transitioning and could make do with just a pair of good SL skis, aim to have one pair of SL (of a length between chin and nose) and one of GS skis (length between eye level to just over their head) by the time they're 12.
The boots are now a little more important, as their feet get stronger. You should get them aligned and could fit with custom footbeds - read more about Ski Boot Fitting. Especially as the technique gets more precise, properly fitting and aligning boots becomes important, by 13-14 years of age.
In terms of safety, a hard-ear helmet is mandatory. Shinguards are mandatory, as well as pole-guards. Chin-guards are very good, there will be plenty of drills with full slalom gates.
When you get pole-guards, these go on the slalom poles and you will need a set of poles without pole-guards, for GS training and races where the pole-guards are not allowed. Also, pole guards should not be used in free skiing, as they affect pole planting - so either use the GS poles for free skiing or get three sets of poles.
When selecting the helmet, look for the possibility of attaching chin-guards to it soon: some models are more hassle or the guards a lot more expensive than others.
See more details Ski equipment and tuning for U12 and U14.
You need one pair of SL (length between chin and nose) and one of GS skis (between eye level to just over their head). If you want to participate in specialized races like FIS, you need to read the respective rules for equipment selection (length, radius etc).
You may want to look at an pair for SuperG or rent one when needed.
The only reason to get two identical pairs of either kind of skis (SL/GS) is to save you some Saturday nights, if you have to tune before a race. If you do get two pairs, make sure they are identical and you use them equally for racing and training throughout the season: do not keep a "race" pair, which will always feel more sharp and different from the other one.
Likewise, keep the skis tuned properly all the time: you don't want the the skis to feel all of a sudden too sharp or too fast on race day - keep them sharp and fast all the time.
The boots are now very important, as they build precision and specialized skills and need perfectly aligned, canted and fitted boots. You should get them aligned and fit with custom footbeds by a serious boot fitter - read more about Ski Boot Fitting.
In terms of safety, a hard-ear helmet is mandatory. Shinguards are mandatory, as well as pole-guards. Chin-guards are mandatory for full slalom gates. Also, elbow-guards for GS are good to have.
Perhaps spine protectors and some body armour (look at a "GS suit"), if they'll be doing a lot of speed.
Make sure their gloves are the heavier-duty race kind, as they will bash fingers against gates, occasionally.
See more details Ski equipment and tuning for U12 and U14.
The skis should be race skis, according to the age/size of the athlete.
To encourage learning, a softer race ski is recommended, i.e. not the full World Cup racing ski from any of the manufacturers, but the one model down - it is usually easy to figure out which those are. They are often called "masters racing ski" or such or just ask at the store.
A full WC racing skis is very stiff and requires a lot of technical skill and power to use, otherwise it will not reward the skier with the right experience. So look to move to this level as technical precision becomes apparent and so is the strength of the athlete.
At the same time, do not get a consumer ski - these are generally too soft for the ice/hardpack that training and racing is conducted on and will equally retard learning.
Have at least two sets of winter gloves and specific ski socks per kid - they will get one wet quickly. Also, hand warmers and boot warmers will keep them going for a bit longer on cold days.
Boot dryers are home are excellent to dry the boots overnight - the boots will always be wet after a day of skiing. Forced-air vents work well also.
Many racers prefer to train and race in specialized ski racing suits.
Have a set of poles with handguards for SL and a separate set of poles without handguards, for freeski. Also, specialized GS poles are important: don't use SL poles when skiing a GS course, because you'll loose the baskets and may be kicked out of training.
The poles should not be too long or too short - the more common way to measure the poles is to flip them over, hold them from under the basket and have a length that will allow the elbow to bend at 90 degrees.
However, racers prefer longer poles for GS, to get a good kick out of the gate and on gliding sections. Also, advanced skiers prefer shorter freeski poles, which work better from a generally lower overall stance...