Whilst I don't live in Sydney, most of the below can be applied there:
Groceries: Yep, Aldi's pretty cheap and decent quality, and keep an eye out for specials at the big two (Coles/Woolworths). Often markets or local fruit/vegetable shops or butchers are cheaper still for fresh produce.
Phone: There's plenty of prepaid or SIM-only postpaid deals which are cheap enough. Depends on which network (Telstra/Optus/Vodafone) works best in your area (and your phone), although they all should work fine in the cities. You might need to note that we don't have any CDMA networks, so if you're looking to bring over a Verizon/Sprint handset, you're out of luck.
However, many mobile plans here operate on a 'cap' system, where $x will get you $y in 'value' (ie: $500 of value on a $50 cap) for calls/messages (outgoing only, incoming is free). Now, those calls and messages are charged to the cap at rates of near a dollar a minute and ~25c a message. Guess what happens once the 'cap value' is exceeded?
Internet: TPG or Exetel are probably a fair whack cheaper than the big players. Basically as far as landline-based internet goes, ADSL is far more common here than cable (which is only available in the big capital cities, and you're tied to whichever provider owns the infrastructure). There's heaps of ADSL providers (mostly resellers), you could check Whirlpool (
http://whirlpool.net.au) for more info.
Craigslist: We have Craigslist here, but from what I can see, it's virtually deserted. Gumtree is far more popular (or eBay).