Third point to consider, skill level. That is to say, they must have the skills to capture photos under any lighting condition. For instance, some wedding photographers will only work with natural light. But be careful with this. As they must have the equipment that allows them to work under extreme lighting conditions.
Consider this, if you like natural light, but part of your wedding is at night, ask them to show you work that they have captured at night. This will give you an idea of the result you will have for your wedding.
Also, there are photographers who use both natural and flashlight. Allowing them to cover any type of event, day or night. Moreover it allows them to make creative images using external lights.