I use a standard 5 gallon bucket, it is good for a day and a half before refilling. But the size of the container really depends on how many nozzles you are using, how long you run your mister and how often you want to refill your container.
I don't mind filling daily (part of my routine), since I know the water is always fresh. I also rotate out the bucket once a week to let it get a good bleaching and airing out.