OK, I'm a bit outside Sydney (1.5h north) and have been here nearly 2y. In that time we have seen several redbacks, mostly in the crevices in outdoor toys (I have learnt that the really scrappy cobweb with bits of leaves in denotes redback territory) so the toys get hosed out before use and then the spiders are stamped on. They're very slow moving so easy to kill. I had one in the house but just inside the back door - shoe took care of that very easily. they like dark, quiet crevices where they're unlikely to be disturbed, so it's better not to leave shoes/boots etc. outside.
So far still haven't seen a funnel web and we're very close to bush, and our garden is pretty bush-like itself. Am a bit nervy of those, I have to admit - especially after I read that they can live in swimming pools as well!!
If you DO ever come across one, don't try to beat it off or kill it, trap it in a jar with a lid and take it to your nearest hospital, so they can extract the venom for making more anti-venom.
We have had a few huntsman spiders but although big, they're not really dangerous unless you step on one or trap it - the bite can be painful but not really venomous (although of course you have to watch out for infection)
White tails - varying reports of the danger levels of these spiderbites - an Aussie friend here was bitten by one 10 years ago and still has occasional trouble with the wound site but research says that it's not really a problem. I would still kill one on sight if I saw it and I know people here who have their houses fumigated if they see one indoors.
Mouse spider - you don't want to tangle with that one either, but it's not really venomous, just aggressive and painful.
I have a DS who is now 3.8 - he was taught as soon as we got here not to touch anything in the way of creepy crawlies in the garden. Of course, MIL is a lot more blasé about the situation so encourages him to pick up moths and the like but I stamp on that concept asap because of course DS couldn't tell the difference between what is safe to touch and what isn't.
Snakes - the only one we've seen in our 2y here is a baby red-bellied black snake that was dead, probably dropped by a passing kookaburra (we have LOTS of those in our area, they eat the little skink lizards in the garden).
Our current biggest nuisance is a bandicoot which is making a real mess of our back lawn by digging it up all over the place - it's a kind of rat thing, we have a trap out for it (we're going to relocate it to some deep bush not far away) but so far no joy. They're pretty dangerous to handle, apparently, but you won't see many of them!
HTH :)