Anyhow, we sought some professional advice from a pest control agent. After he fumigated our house he passed on some really simple yet valuable tips which I've included below:
Keep all food covered or put away at all times, and that includes the fruit bowl. Kids are always prone to grab an apple or handful of grapes and eat them without giving washing a second thought. But apart from the obvious, if there's nothing to eat, the pests are discouraged. At the end of the day, most insects are looking for grub and that includes cockroaches. Check and clean under washing machines, fridges, and ovens. You could be surprised what you find.
Make sure you clean up as you go along. It's too easy to grab a sandwich and think about cleaning up the tops a little later. In the middle of summer, just 30 minutes or less of fresh food lying around is enough to have your house invaded by armies of ants, flies and the like. Also check and recheck that there is no food dropped onto the floors as this is where the cockroaches love to scavenge. Once those critters start breeding you'll most likely need to call the professionals in to finish them off.
If you have animals, make sure their eating bowls are cleaned or covered up after meal times. Cats especially tend to leave half eaten food in their dish and this is very attractive to flies and the like.