Tickets prices for public transportation in Zurich can be found here:
Tickets - ZVV.
Be aware that regarding fares, Zurich (110) as well as Winterthur (120) count as two zones.
For your travel arrangement, I would recommend to buy two day passes for zone 110 (1-2 zones fare) and one day pass for zones 110 & 121 (3 zones fare) for your trip to Wallisellen (121).
This should cost CHF 31.20 (2 x CHF 8.80 + 1 x CHF 13.60) according to the following price list:
Day pass - ZVV.
Prices assume you travel 2nd class.
You can buy those three day passes in advance, they will become valid upon stamping ('Tageswahlkarte'). I would recommend to buy the three day passes on arrival at either a ZVV or SBB ticket counter. You will find one at Zurich airport as well as at Zurich main station.
There are other options, which may be marginally cheaper, but they would require you to buy more tickets or they would limit how long you can travel in each zone. (You stated you would rather want to buy less tickets for convenience.)
Be aware that using public transportation during nighttime may lead to an additional surcharge of CHF 5. You can find more information on the night supplement here: Night supplement - ZVV.