Hi Marko,
Yes there is a rent shortage in Sydney because not enough houses or flats are being built to cater for the growth in people moving to Sydney. But it's not that bad. You should be able to find a good one bedroom flat or apartment near the city. It all depends on where you want to live but expect to pay anything from $300 to $450 for a decent one bedroom place. That's assuming you end up near the city centre. The thing you should know about lots of flats in Sydney is many of the older flats were built with thin walls so you can hear your neighbours. I have a neighbour upstairs who has a tile floor and he rises early. He is always dropping something on that floor or dragging things across at 6am. So, be wary of that. Try to get a flat on the top floor, or go for a house if you can afford it. You'll get a better night's sleep. Otherwise invest in ear plugs.
As for the weather - January is horrible. it's very humid. The humidity kicks in in December and goes to about February so make sure you find a place where you can create a breeze in your flat with windows at either end. Try to avoid ground floor flats that are built right on the ground. They tend to be damp.
Bus or train? I think being on a train line is much better but sometimes you don't have a choice. the best option is to find a place that has both a train service and buses. Sydney has lots of buses that service the inner city areas.
Places like Bondi Junction and Chatswood have plenty of transport options.
If you want to find out where the train stations are, go to
www.cityrail.infoGood luck.