I second the vinegar and water. Sprikle bicarb/baking soda on the bits that are particularly dirty, then either mix a couple of capfuls of white vinegar into half a bucket of water and mop away. Rinse afterwards with hot water. The vinegar smell will only last a short time, but it works a treat.
Then again, don't go overboard with cleaning. A "clinically" clean environment means the child is not exposed to any germs. This can mean its immune system doesn't become as strong as it should.
Our kids have never been sick (26 months and 8 months) barring one mild cold and they have certainly licked their share of floors. Not that we encourage it, but you can't watch them 100% of the time. ;)