Ideally, a battery bank should be sized to be able to store power for 5 days of autonomy during cloudy weather. If the battery bank is smaller than 3 day capacity, it is going to cycle deeply on a regular basis and the battery will have a shorter life. System size, individual needs and expectations will determine the best battery size for your system.
Banks larger than five day capacity are generally more expensive than a back-up power source, like a mid-sized generator. Occasionally there are situations that require a larger battery bank to meet the surge load when starting (like large well pumps or stationary power tools).