Definitely avoid Telstra for your mobile, they're worse value than the rest. 3 are pretty good, as are vodafone. Coverage isn't a concern, it's all good everywhere in the cities. However if you have to go bush at all then go with Telstra.
Cap plans are similar to what exist in the UK, you might pay $49/m, and that gets you $300 worth of credit, to be used on calls or texts, as you please. Same idea as here but you get the flexibility between calls and texts.
North shore is great, I lived there for many years, near Chatswood. With the Tunnel and the Eastern Distributor it's not that hard to get to the airport, my old man does it weekly and it's perfectly fine. For getting to Hurstville - it's probably about 40mins (non-rush hour) from Chatswood. I used to visit my sister in Rockdale and it wasn't bothersome. I wouldn't go much higher than Lindfield though, purely because of the commute.
I can't comment on LAHFA details, but this would be a good place to start:
http://www.lafha.com.au/Home.aspx