Welcome to Hong Kong. Here are some things that took me a while to figure out, which I wished I knew right away:
1. Find a place to live so that you'll have a permanent address. You'll need this to get everything else;
2. Get your family's immigration status sorted out right away - namely get your HKID cards, as all legal residents are entitled to the benefits listed below;
3. For senior citizen family members, get them a senior citizen card, which will entitle them to a host of benefits, including a special Octopus card which automatically charges them half price for the MTR, bus and tram;
4. For pregnant women and pre-school age children, register at your nearest Maternal and Child Health Clinic, which will entitle them to free ante-natal check-ups, scans, tests, vaccinations, etc.;
5. For pre-school age children, obtain the Pre-Primary Education Voucher, which will heavily subsidize pre-school fees at qualifying local schools;
6. Shop local - local supermarkets, wet markets, butchers, pharmacies, etc. Prices are much cheaper than at the chain stores for everything from diaper to detergents. A good local supermarket is Kai Bo Supermarket. Prizemart also sells many foreign products in bulk. Also, note that if you order from the chain supermarkets on-line, the prices are their "weekend" prices, which is higher than their weekday prices; and
7. Carry your own bag. Hong Kong chain supermarkets and chain pharmacies are not only more expensive, but will charge you by the plastic bag your use, so bring your own.
The weather is great right now, so take advantage of it and walk everywhere! My favorite neighborhoods on the Island is North Point and Sai Ying Pun, which is far less gentrified/expensive than Mid-levels and Wanchai.