Sounds fperfectly feasible.
Trains probably best to get snow n rail tickets . This gets you 20% discount on train (on top of any concessions the kids might be entitled to) and 10-20% discount on skipasses. And 15% discount if you use the intersport ski hire shop.
There might be other better deals for trains such as family tickets but I dont know about these.
Where to go. I go to Engelberg a lot they do have a good beginers area but it is quite separate from the other runs. So I would say that the comments from Ace1 and Richdog are valid. ie If you are a complete beginner then Engelberg is fine but if you want to get away from the beginners area then the rest of Engelberg I would say is a big step up- virtually all are red runs, and often not freshly pisted, which can be diffficult for early skiers.
Other options/saving money:
Engelberg Lift pass is on of the more expensive, though If you are just in the beginner area there is probably a cheaper option.
For alternatives, look here http://swisswintersports.co.uk/getaround.php
and click on "Selected resorts from Zurich by public transport" then "least time". You will then see all the other options close to Zurich.
Zurich is also close to Austria. St Anton and other resorts are not very far by train.