I probably started looking for accommodation two months before my arrival in Sydney. But actually that's not really how it works over there. It feels like all Sydneysiders are always looking for a new place to live and finding a flat just one or two weeks in advance is normal. I found my room two days after my arrival and I moved in two days after that!
I was lucky to have my sister living in Sydney so I stayed with her the first days. If you arrive one week before you start in your lab, then it would probably be a good idea to stay in a hostel. The 24/7 parties going on there could be both good and bad. Good if you want to meet new people but bad if you value your beauty sleep.
I ended up staying in Bondi and I paid $350 a week (madness!). The room was fresh which is pretty rare in the Eastern Suburbs. I had many restaurants just next to me and I loved living in that area. One advice from me would be to live close to train stations since commuting in Sydney is quite frustrating. I used to walk to Bondi Junction and take the bus from there since it would be just a fast as sitting on the crowded bus. I lived with one guy who was working nights at a hospital so most of the time it felt like I had the entire place to myself. If I was going to do it again I would probably try to find a room to share with people in my age. There's just difficult to find a place with students, since there's so many people living in Sydney just for the lifestyle and has a lot of parties going on. So think about what kind of people you'd like as your roommates!
I suggest checking out flatmates.com.au which seemed reliable when I was searching for a place. Gumtree is very suspicious and I would not recommend finding something there, even though some ads probably are legit. I think the Facebook group "Svenskar i Sydney - boende" is a really good place to find accommodation on.
I know UNSW offer on-campus accommodation which is just as expensive as any other place but apparently food is included. There are mainly international students who just left their home that stays in that type of accommodation.