Starting out, use what you have
This is where ski racing can get expensive. In the first few years of skiing, one set of skis is just fine. As they advance, different skis are needed for different events. We train mostly Slalom as we are at a small hill. Gold team members will need skis for each event they plan on competing in, for us that is GS and Slalom. Obviously first season is a great gauge of racer interest. Be sure your racer is really into this before buying a lot of equipment! There is definitely someone with used gear looking to trade or sell! We also have a team swap page for trading or selling to other team members.
If you are looking for used and its not available within the team, check out SideLineSwap.com. Its a site similar to ebay for used sports equipment.
The competition guide is published each season if you are registered with US Ski and Snowboard, there is a detailed specification in the back. Here is a PDF outlining gear needed for racing at the US Ski & Snowboard level in different age groups:
Kids grow, so keeping up with them can be tricky! Skis that are chin to nose are great for Slalom. If you are buying, find nose hight, if you are hoping to get another season out of them, chin is fine. We understand needing to make things work, even shoulder hight is manageable, particularly at the younger ages. Once your racer gets to U16 or even U14, ski sizes get more event defined, see the competition guide for that.
With Giant Slalom (GS) skis are longer. These tend to be eyebrow hight to a few inches taller than the racer. These are great skis to have, most all mountain skis are built from GS specs with some modifications usually to the width. If you're traveling to Colorado, Utah or other bigger mountains, GS is the ski to take. Like Slalom, as the racer gets older and attends USS&S or even FIS races, events determine ski sizes.
Generally keep race skis out of the park. Sliding a box a couple times a season and grabbing the occasional air isn't an issue, its the ongoing abuse that adds up. May want to get some park specific skis if you have a racer than just can't keep out of the park. We do some training in the park, mostly on the landing of the big kicker. Skiing over that creates a floating stomach feeling and some kids end up in the air, though only a few inches off the snow, they can be in the air for a distance of a few feet. Getting them comfortable with drops and rollers is important, we find that terrain in the park. It's the rails, box spins, and big air that tend to make a mess of skis. Rails scratch the bases and bash edges, box spins catch edges and rip them out, bonks delaminate tips and tails, big air landings can delaminate bases. Not things desired for race skis, park skis are better built for that.
For Gold team, there are 3 measurements to look for in skis; length, width, and radius. Slalom skis will be 130cm-165cm in competitions and a max of 65mm underfoot for FIS but no limit for other competitions. The radius is not defined but tends to be from 8-13m. GS skis only require 17m radius until FIS then length and width are defined.