There are a number of good brands out there, basically all the helmets at a ski shop will protect you. Boeri, Giro, Leedom, Briko, Joffe are the names I see most. The key is to find the helmet that fits your head. Just as some footware is good for people with high arches & another is good for narrow heels, helmets also give a different fit by manufacturer and by line. Some are good for rounder heads, some for more oval heads. You have to try on helmets, not go with one type that's recommended by someone. In my family, Briko fits me and my husband and daughter wear Boeri.
The helmet needs to fit tightly. No hats underneath, but a balaclava or turtlefur's shelaclava is great.
Try on helmets even if you hate the color or graphic. If it offers the best fit, the shop can probably order one in the correct color for you. The shop should measure your head first so you know your size.
There are also different styles, full helmets, shorties, helmets that are somewhere in the middle. If you race or go on expert terrain, get a fuller helmet. Actually, as far as I'm concerned, get a fuller helmet no matter what you do. If you want to protect your head, then protect it.