Hi,
We are British and moved back from Melbourne a couple of years ago after four years out there. Things changed a lot whilst we were out there, but basically we found utilities to be expensive (gas, electricity, water, phones, broadband), cars are expensive to buy but cheap to run, housing used to be cheap, but is now stupidly expensive within 10-15km of the city centre. Local food in season is cheap, imported and processed food (including chocolate!) is expensive, but eating out, and coffee, is generally cheaper. Public transport is quite cheap too. Very few of my friends still living there can afford to buy houses, many are moving out to small country towns.
Melbourne is a funny place to live, mixture of amazing and awful. The footprint is about the same size as London, so it can easily take an hour's drive from the city centre to the edges, even on the freeway. Which can be a shock if you've lived in a smaller town in the UK. Oh, and no roaming on footpaths in the countryside - stick to footpaths in the National/State parks only!
The best places to live are down by the beach, so you are about 10-15km from the CBD, with public transport access and good bike paths (cycling is fast becoming the easiest way to travel around the inner city). You can be 30 minutes from town but then have the open space of the water front close by. But, don't expect a big house, pool and garden. To get that you'll need to be out in the 'burbs, which means LONG commutes from the CBD and being surrounded by neverending housing. The far north and east of the city towards the National Parks are quite nice to live in, but again, long train commutes into the CBD.
There are some good State schools, but many middle class parents choose the Catholic schools which are lower fees than the private schools but better quality than State schools, only downside being the Catholocism! But as a rule, don't expect a high level of literacy from childeren in Aussie schools!? (Expects to offend someone, but I found it to be true!)
On the plus side, there are gorgeous 50m open air/indoor swimming pools all over the city so if you like a swim it is a great place to be. Coffee is also generally good, and cafe breakfasts are looooovely!
And remember, Melbourne gets VVVVVV cold (and dry) in the winter. 4 degrees there feels like below zero here. Also, they aren't into double glazing and central heating is unknown, so your house will be cold. Your backyard pool will be appreciated when you get weeks in the 40's though. Oh and the sea around Victoria is cold. All year round. Very similar to the south coast of the UK.
Sorry, didn't mean to write an essay, but always love to remember my time out there! Enjoy :)