You've been watching too much 'nature' television which loves to go on and on about how dangerous and scary Australia is or you've been listening to people who've been pulling your leg. The USA has many, many spiders, lizards and large insects too and they don't bother you there do they? Same in Australia - they're there, but most people never come across them.
We do have some pretty big spiders, but they're completely harmless. I don't like big spiders either, but very rarely come across one and in 6 months here, you'll be unlucky to see any.
Most houses don't have geckos, but if one that you're in happens to have some, you'll find them to be gorgeous, harmless little lizards with big eyes who EAT spiders and other insects and creepie crawlies! Geckos are your friend because of their diet and in any case, they're terrified of you. You won't find one closer than several metres away and it will either be sitting absolutely still hoping you don't notice it, or it will be heading in the opposite direction at a rate of knots.
I've never seen a giant insect inside my house and I live in a bush area so you're even less likely to see one.
Stop worrying and come and enjoy our lovely city (Brisbane I believe?).