Moonee ponds is a good suburb especially for what you need, you will get a little more space there than in Flemington, Travancore or ascot vale. Moonee ponds is where we do our grocery shopping there's a Aldi, Woolworths and Coles there aswell as other smaller shops.
I found this site really helpful as the primary schools are zoned so even if you were paying international fees you still need to live in the zone for that school. (http://melbourneschoolzones.com/schools/moonee-ponds-primary-school/)
There is very few options for childcare in australia especially for shift workers, I worked in hospitality before having my kids and have been unable to go back to work due to the lack of options!! Your best bet would be to find a family day care to do pick ups from school clubs, another option which may work would be to advertise for a au pair in your area who wants to get some extra work by doing school pick ups, depending on the family's they are placed with they may not be needed at that time and are looking for extra work, Iv found the Facebook group "AU PAIR in Melbourne" handy for this. Also there is another Facebook Group called "Moonee valley Buy swap and sell"which can be helpful finding childcare, looking for advice on the area and picking up some nice second hand furniture for your house.
NIB insurance does have ambulance cover but even if it didn't it's only $80 a year for a family, the NIB cover worked out the most cost effective option for my father at $70 per month for basic cover as he will be staying for a year on a tourist visa, there are a number of different company's which offer this type of cover though.