```python
def driest_window(rain: list, width: int) -> int:
    if not isinstance(rain, list):
        raise ValueError("rain must be a list")
    if not all(isinstance(day, int) and day >= 0 for day in rain):
        raise ValueError("all daily readings must be non-negative integers")
    if not isinstance(width, int) or width <= 0 or width > len(rain):
        raise ValueError("width must be a positive integer less than or equal to the number of days")
    
    if width == len(rain):
        return 0
    
    min_sum = float('inf')
    min_start = 0
    current_sum = 0
    
    for i in range(len(rain)):
        current_sum += rain[i]
        if i >= width - 1:
            if current_sum < min_sum:
                min_sum = current_sum
                min_start = i - width + 1
            current_sum -= rain[i - width + 1]
    
    return min_start
```