I agree with the principle that only you can decide what is a good area and suitable for your family, however if you could be driving to the North or south each day and unless you love driving then try to live as centrally as you can, these areas are more expensive but could save you so much time in travelling. From Gawler to the North down to Aldinga in the south is only 80k but will easily take 2 or more hours during peak times and not much less off peak. In Alelaide we don't have anyroads that can get you round the city quickly and easily, as such any lengthy drive will encompass endless traffic lights. I drive 40km to work and I pass through 36 sets of lights and 2 level crossings, and these are the main roads. And living nearer the city will give you so much more to do with everything based in the city or very near, Football, AFL, Cricket, festivals, there is always something happening in the city.
We're in Mawson Lakes, a very modern development with everything within easy reach, we're 10 mins from the city by train and less than 15 mins to semaphore beach, but with your budget, work and requirements then Grange, Henley Beach, West Lakes may be better placed.
Our home insurance is with AAMI, they offered the best package for specifics we wanted insured, but there are cheaper ones, our cars are now covered by ANZ, but like the UK, shop around, they seem to take in turn for the offers to win business.
Our internet is with Telstra, I know that these are typically the most expensive, but we have our foxtel, mobiles, home phone and broadband with them, and with the complete business I have negotiated preferential rates that other providers can't get close too. A friend of mine in the industry tells me Internode and TPG are ones to go with these days though, but i cannot recommend them personally.