Hello travelskier
There is not much choice. For the way from Zurich Airport to Zermatt, you have to purchase a point-to-point ticket at CHF 130.00 each, 2nd class. Avoid the purchase of Supersaver tickets, these are only valid on the selected connection and will be lost in case of a late arrival by air (unless you plan a buffer of at least 2 hours, but you could not travel earlier if you arrive on time).
For the return, you can purchase a Saver Day Pass (which isn’t available any more for 30 March). It costs CHF 79, you have to save that pass as soon as practical as they can sell out and certainly will, given the Easter weekend. The Saver Day Pass is valid for any connection on 6 April.
https://www.sbb.ch/en/tickets-offers/tickets/day-passes/saver-day-pass.html
Purchasing the Swiss Half Fare Card does not make sense, you would have to spend a total of CHF 240 per person on train tickets to be break even. I assume for Zermatt you will have a ski pass, so no Swiss Half Fare Card is needed for mountain excursions in Zermatt.
Please let us know if you have got more questions.
Kind regards,
Roland