skiing in Zermatt in February or early March

I am taking my son to Zermatt for his 21st B day but I am finding limited info. any hints on getting there, a good place to stay for a mom and son, so two beds please and any ways to keep to a budget. I know it is an expensive little town but would like to spend no more than say $200-$250 per night for lodging, would prefer to be within walking distance to the main hills. Any hints on best way to buy ski passes, we think we want to include Italy on our pass, I understand that costs more. Anyone who has recently done a winter vacation here I'd love any hints. Thank you. We plan to stay 4 to 5 nights and then go to Germany.