The easiest place to access from Zurich by public transport is Flumserberg - train to Unterterzen, gondola up almost direct from the station.
It's plenty big enough, and they do cheaper limited passes that only cover the easy slopes for the first few times. You can book individual lessons, I don't think they do adult group classes, so learning ski and snowboard separately will cost (same anywhere!).
If you want to do it fairly socially the International Ski Club of Zurich does four weekends in January. http://www.iscz.org/ski-and-snowboard-school-1