(1) House / Hotel / Serviced apartment
Before you arrive to Melbourne, in case you don't have somebody to "host" you for a while, you need to organize your initial stay.
You'll see that you have a few options : it is difficult to find a house when you are here... so "remote" it should be much more difficult (in case you don't have a lot of money to buy one) .. so you can search for a hotel or for a serviced apartment.
We've heard about the serviced apartments at Darling Towers in South Yarra :
- they offer serviced apartments in a few locations near City centre.
- the prices seams to be acceptable from what I've found
- the conditions are very good & the position of the apartments is good for a newcomer (that doesn't know the city)
and decided to go there.
We made a reservation for 2 weeks.
Please consider that you need to provide a valid card to do a payment to validate the reservation.
From here (for example they have locations on Darling Street, on Caroline Street) you have direct connection to the City centre using tram 8 (I think it takes 15-20 minutes)

or with the metro at South Yarra station to a few locations within Melbourne (the white line is the tram line and the arrow shows the direction to CBD and the red X is the South Yarra metro station).
You can have also internet connection in this location (it is not so great, but at least you can search for a house or for a job).
Also on Darling Street or on Caroline Street that are a lot of serviced apartments that you can consider.