```python
def driest_window(rain: list, width: int) -> int:
    """
    Find the starting index of the width-day stretch with the smallest sum in the rain readings.

    :param rain: List of non-negative integers representing daily rainfall readings.
    :param width: Positive integer representing the number of consecutive days to consider.
    :return: Starting index of the driest window.
    :raises ValueError: If rain is not a list, any reading is not an integer, any reading is negative,
                       width is not a positive whole number, or width is larger than the number of days.
    """
    if not isinstance(rain, list):
        raise ValueError("rain must be a list")
    
    for reading in rain:
        if not isinstance(reading, int) or reading < 0:
            raise ValueError("all readings must be non-negative integers")
    
    if not isinstance(width, int) or width <= 0:
        raise ValueError("width must be a positive whole number")
    
    if width > len(rain):
        raise ValueError("width cannot be larger than the number of days")
    
    min_sum = float('inf')
    min_start = 0
    
    for i in range(len(rain) - width + 1):
        current_sum = sum(rain[i:i+width])
        if current_sum < min_sum:
            min_sum = current_sum
            min_start = i
    
    return min_start
```