H202 (hydrogen peroxide) is hands down the best for this, IMO. It is very effective against both bacterial and fungal growths while very safe for humans and plants.
If you have any kind of porus material (drywall, wood, etc.) H202 is better than bleach because (according to research, not me) H202 has much better penatration, where bleach only disinfects the surface.
My grow area is small, but I had to fight an extreme mildew problem in another very large room, and I learned that there is often an even bigger infestation on the side of surfaces you can't see.
One thing about H202 to keep in mind. It starts to degrade (turn in to water and oxygen) the minute you break the seal (even after closing). At that point you should use it up within 6 months. So it doesn't make sense to buy it in huge containers and store it. Better to buy lots of smaller bottles, unless you will use most of it all at once.
[Edit: vinegar and water mix is also an effective, cheap, and organic alternative. It worked well for me also but not quite as well as H202, plus it stank, but you kinda get used to it.]