Expect to be annoyed by the trains - they're no where near as clean or efficient as Hong Kong!! It depends on where you are going, but if you're going away from the city a bit, sometimes the trains only go every half hour or something crazy - so it's more important to check out timetables!!
http://www.cityrail.nsw.gov.au/
They do have a train from the airport to downtown. It's not an "express" one like Hong Kong though - the airport is much closer to downtown but the train still takes probably half an hour (and doesn't leave as frequently either!!)
I've never taken a stroller on the train, but most stations do seem to be pretty accessible for that kinda thing... I DO think that Sydney is MORE stroller-friendly than Hong Kong!!