I also think a waterproof outer layer is important.
Your clothes don't have to be expensive brand names. For a trip to Colorado last year, I used a relatively cheap parka I got from Walmart and an old ski bib I bought used from a rental shop years ago as my outer layer (ski bibs are basically insulated, waterproof overalls). Make sure your gloves are warm and waterproof as well - with no fabric to soak up water around the wrists. A balaclava is very nice to have, too, especially if it gets windy, particularly up on the ski lift - and a balaclava doesn't have to be overly expensive either. Under the outer layer, I tend to just wear sweatpants, a knit shirt, and a fleece jacket or sweatshirt or two - the trick is to have layers you can add or remove as necessary. I'm not crazy about long johns, and haven't had a problem wearing cheap, plain old (even cotton) stuff instead of the high tech wicking stuff many people recommend. (If you were going backpacking or mountain climbing in cold weather, you'd probably want the high tech stuff, but you're not going to be that far away from the warmth of the ski lodge, especially if this is your first trip and you have young kids. You will need goggles, too (don't need to buy expensive ones in my experience), and don't forget to use sunscreen and Chapstik.
The resorts out there should rent or sell everything you need, but might be higher priced than you could find elsewhere. Maybe look for sales at Dick's Sporting Goods for balaclavas and gloves and goggles - though I have used cheap Walmart gloves too. You might find a Walmart out there to see what they have - Walmarts near the ski places in Colorado will tend to have ski stuff that Walmarts elsewhere won't carry - but you don't want to waste any more time out there shopping than you have to.