Arrived on Thursday last week - some things that helped me find my feet:
Phone - get an Optus simcard from the airport - $20 for $80 value - oinstant phone number - remember to unlock your phone before you come. You need a contact phone no!!
Mobile broadband - any operator for the city, Telstra (or Vodafone from August) for the hills - check with suppliers! All the mobile phone companies located on Rundle Mall.
Bank - Westpac migrant branch on Gouger St, interview lasted an hour, got registered for internet bnanking and shown how to use it by Ryan (good guy!) plus all the places in the city I would need to visit to get registered/do stuff. Top service! Register and open account before you go.
Medicare - Currie St, select register on the computer as you walk in, take a number. Took 20 mins all in, figure an hour for a family. Bring your medical notes and NHS no - you will definitely need an NHS card if you qualify for reciprocal agreement with UK.
Mail boxes if required - Post office in town or any post office location will advise.
Tax file no - apply online the day you arrive - you need an address for them to send the number.
I stayed 2 nights in the city, got all my stuff done, then moved to Glenelg - great vibe!
Jobs - sort as much as you can from UK - much easier to come here for interview than search when you arrive.....got one on Monday night.
Rentals - compile a list from realestate.com.au if not sorted from UK - shoot round them by car, as some are well dodgy, some really nice, then ring agent for viewing.
Maps - get a UBD from Dymocks or Borders on Rundle Mall. Indispensible.
Car hire - Aussie car rentals on Brighton Rd, don't need a car until you are ready to look for rentals - first couple of days are recovery from flight/in city for admin.....
Lastly jet lag - walk a lot, try to stay up, accept it will be a few days before you get a complete night's sleep. There are lots of coffee shops...........!