Hi there,
I'm in Ontario but I used to live in Edmonton. That was a while ago though so I'm trying to think.
I would say your number 1 priority is to find somewhere to live. Calgary is pretty expensive and my understanding is that there aren't a lot of properties available so you might want to start looking now. If you are buying, you can check www.mls.ca for listings, and for renting I would check the local paper (Calgary Herald I think?) or kijiji (www.kijiji.ca). Kijiji can also be a source for cheap(er) furniture and vehicles when you first get here as well.
I have 4 children as well and I have found it very difficult to find houses with enough bedrooms so that everyone gets their own! Most houses here seem to only have 3 bedrooms and you'd be lucky to get 4. 'Tis weird!
Health care is covered by the province so each one is different. There will likely be a 3 month waiting period between the time you arrive and the time your health care coverage kicks in, so during that time if you need to see a doctor you will have to pay out of pocket. After that it will be covered. Again, each province is different so not sure what exactly will be covered for you. You may also need to pay for the health care coverage (in Ontario it's based on your earnings, on a sliding scale). Bottom line - if you have any ongoing prescriptions make sure you bring enough with you to last until you can see a doctor!
Not sure how Alberta is but here in Ontario we have a shortage of family doctors so you may not get a family doctor right away.
The school year starts the Tuesday after Labour Day, which is the first Monday in September. Likely there won't be anyone in the schools until the last two weeks in August so you will need to wait until then to register. If it's like Ontario, you won't have a choice of what school to use, it will be the one closest to your home. School runs September to June, 2 week break at Christmas, 1 week off in March, and assorted single days off here and there.
Not sure what else to tell you?
Oh, when you are buying something in a shop, the price on the shelf is not the price you will pay at the till! Tax is added at the till so you need to do some math, in Ontario it's 13% but that is a combined provincial and federal tax, in Alberta they only pay GST which is 5%.
I will check the thread later so feel free to ask me something! Good luck with your move!