Was in Zermatt January last year: magnificent resort. Part of the charm to mine was staying in Zermatt proper which is a beautiful village and gives access to the 3 main lifted areas. Adding an (expensive albeit short) train ride each day doesn't make much sense to me. I think ponying up the extra $ to stay in the village is worth the spend. We found some semi-reasonable airbnb accommodation in a central location which didn't break the bank (bearing in mind Zermatt is an expensive resort mainly due to the strong Swiss franc and high tech/super modern lift system). If you're looking to save some $ consider staying on the Italian side of the Matterhorn # Cervinia, facilities/lifting no comparison and more mellow terrain but worth considering.
Tasch is no more than a huge car park for travellers from all over Europe. Stay in Zermatt it's worth it. There used to be a Youth Hostel there, with relatively cheap accommodation. It's still Switzerland and Zermatt, so not cheap.