I most certainly won't be looking forward to funnel webs though... Yikes! Spiders just creep me out entirely!
You're lucky then, funnel webs are predominant in Sydney.
We just have snakes, redbacks, european wasps, more european wasps (come and take the bl**dy things back you b*ggers!), etc down here in Melbourne, (as well as some excellent four-wheel driving).
As for beaches, the Mornington peninsula both bay and ocean side. Or travel a little further east to Ninety Mile beach/Gippsland Lakes or west down the great Ocean Road to Apollo Bay, etc, etc.
Regarding internet, basically you're screwed - welcome to the real world.
Although when you get here and have a place go to Whirlpool and use their plan finder to find an ISP but whatever you do, DO NOT choose BigPon
EDIT: Oh yeah, regarding the spiders please don't hurt the Huntsmanw spider if you find him in your house, just pick him up on a broom or something and stick him outside. They're not poisonous and do a good job wandering around eating insects although they do get rather large so you might be surprised by one staring down at you while sitting on the toilet.
You'll also get the shock of your life when you flip down the sun visor in the car and have one drop in your lap