@JoannaSQ. Start checking out Sierra trading post. Sign up for Active Junky which is a free shopping club and save an additional 8-10%. Campsaver and ski essentials has some great deals as well. There are still good deals there. Not sure what you consider cheap
I get it if you are on a tight budget but be careful not to buy something that's not going to keep you warm and dry or not have any wind protection. You pay a ton of money to ski so don't end up miserable or frost bitten.
Look for a minimum of 10k h20 proof and 10k breathability . Gore tex is rated at 20k /20k and neo shell is much higher. Of course materials like gore Tex are good (not very breathable) , neoshell is my Personal favorites and there are other proprietary materials that provide decent performance. Start with a thin base layer That will absorb and transfer moisture to a mid layer that also has these properties. Insulation Warmth is useless if you layers don't absorb and move the sweat away from your skin. The water proof outer protection is known as DWR, durable water repellant, is actually very important and more expensive clothing will have a more durable film but you can buy products like grainger or nikwax that can be applied to less costly clothing to reinforce or revive clothing.
Make sure you have a jacket and pants that meet your needs. You don't need a ton of pockets but at least a couple exterior hand packets and a chest pocket, internally at least one zippered chest pocket. Pit zips are great to quickly dump heat I am a fan of hoods for cold windy days so it needs to be able to fit over a helmet preferably without having to do a lot of adjustments. The zippers should work well and be sturdy. A little soft material at the chin is also a nice touch. I am not a fan of powder skirts but you may like them but a removable one is a nice feature. Bottom hem should have ability to be cinched up.
Edit. Note that the neoshell h20 proofness is closer to 10k.