I have a 10000L tank which is more than sufficient for a household of 4 and some garden. The minimum size is calculated based on your roof surface but normally people install a bigger tank. The extra cost for a few 1000L more really isn't that much and it can save you the cost of a fallback system in case the tank runs dry.
The overflow of the tank goes to a separate sewage system that usually ends in a local stream. This way it doesn't dilute the actual grey/black water which, incidentally, makes a water treatment plant more effective (or so they say). It also allows the water to infiltrate into the ground and there's less risk of flooding the streets during a downpour. At least, this is the theory. Work is still very much in progress to split the sewage systems but we're getting there.