Welcome Dolly,
I'm from adelaide. More information would help, but to answer your questions:
The best places to live depend on what you are looking for, your budget, etc, etc
Adelaide is cheaper than most Western cities, most Australian cities even, but I know a lot of people from non western backgrounds who still find it a lot more expensice than they are used to. Although, once you get a job and are saving, it's not so bad.
Be careful to check that your qualifications are transferable (

although, if you are this advanced, you probably have already). I know this sounds pessimistic, but I know a lot of people who hold professional qualifications who have came here ( or to the UK) and only been able to work in unqualified work ( factories, etc).
How much you will have to pay in education depends on which scheme you are entering the country under. A public Education is free to all Australian citizens ( and refugees) , but can be very costly for some emigrants.
Hope that helps, but, most importantly : Do your homework. Once you've done your homework, go to "www.lonelyplanet.com/thorntree" and ask on the Australian branch.
Adelaide (in general) is a nice place to raise a family, but it does have some areas which aren't so nice. IF you give a list of suburbs which you are considering moving into, perhaps we can give better info.
It's hard to know the answers to your questions without knowing more about your situation. If you have any specific information feel free to pm me.