Hello Glen, and welcome.
What is your daily journey? I assume it is a commute to and from work within the greater Zürich area. Plus evenings and weekend shopping and leisure, also within greater Zürich.
In that case you need an "Abo" for the ZVV (Zürich transport district). Start with a monthly, and move up to an annual one. Details are on the ZVV website (it is even in English): http://www.zvv.ch/zvv/en/travelcards-and-tickets/travelcards.html
It is at various prices depending on the Zones you want covering.
Just keep the Abo (plus your "Ausländerausweis" ID card) in your back pocket, and jump on and of any tram, bus or S-Bahn you fancy.
For your weekends, buy a ½ price Abo (Halb-tax Abo, available for 1 year renewable)). This will give you 50% discount for the rest of Switzerland. If you want to come to Basel on a Saturday, just go to your local station and buy a "½-price/Child" ticket from the machine. It only takes about 3 trips to pay off the cost of the ½ price Abo. Details here: http://www.sbb.ch/en/travelcards-and-tickets/railpasses/half-fare-travelcard.html
This is the combination I have, TNW (Basel area) annual Abo + Halb tax Abo for the rest of Switzerland.
As for "Ausland", different rules apply. French TGV's (high speed trains), German ICE's and Italian fast trains all offer discounts for advance purchase. And when you buy a ticket it is only for a specified train.
If you want to got to Paris, there is one train from Zürich every 2 hours, timetable here: http://www.tgv-lyria.com/sites/default/files/pdf/BROCHURES_CO/frequencies-timetable-2017s1-fr_ch-tgv-lyria-en.pdf
Buy a ticket from SBB, at the station or online. Online you get a "print at home" ticket. Be sure to tick the box that says you have a ½ tax Abo, and you will pay 50% to the border at Basel, and from there to Paris a French discounted advance purchase fare.
Germany similar. For Italy there is a catch. SBB doesn't always offers the cheapest fares in Italy. It may be worth splitting the booking.
For lots more good info, see the website: http://seat61.com/