I would argue that bleach is much better at killing microbes than vinegar....My great grandmother died of an infection that could have been prevented with modern disinfectants.

If you're only cleaning, why waste the expensive stuff like chlorhex? Dish soap works great, and soap and water gets rid of 99% of bacteria. If you want to disinfect, follow up with a disinfectant, but be sure to pay attention to contact time. Chlorhex won't do anything for disinfection if you don't let it contact the surface to be disinfected for 10 minutes.