```python
from typing import List

def driest_window(rain: List[int], width: int) -> int:
    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("each reading must be an integer and non-negative")
    
    if width <= 0:
        raise ValueError("width must be a positive whole number")
    
    if len(rain) < width:
        raise ValueError("rain length must be at least as wide as the width")
    
    min_sum = float('inf')
    start_index = -1
    
    for i in range(len(rain) - width + 1):
        current_sum = sum(rain[i:i+width])
        if current_sum < min_sum:
            min_sum = current_sum
            start_index = i
    
    return start_index
```