I am in Sydney for a couple of weeks and tried to take the public transport. I don't know why, but whenever I try other public transports my love towards our public transport back home started to go up.
Be it the cleanliness (I know we are not doing great these days), or convenience, or comfort we are way better. The monthly pass or weekly pass is so damn mixed up you'd end up paying more for this by mixing up the zone system.
The journey time is bad too. Not because of the distance but because of frequency, speed and traffic jams. By the way, understand the Metro bus is 'high frequency' which runs average 15-20 min during peak hours :)
Some tips from my experience is to buy the two way ticket which is relatively cheap. Or they have a pass for tourists for a day with unlimited rides. Get it if you are sure to roam around the city. For longer periods, the myzone ticket is a good bet.
Of course I see the best part of Sydney public transport which is you can get a seat most of the times :)