Choose a photographer whose style you like and primarily base your choice on the style and quality of their photos.
Make sure you can communicate with them easily as being unable to talk to someone will only create an awkward feeling. Better yet if you get on well with the photographer you choose then it’s more likely you will be comfortable with their presence on the day thus leading to a relaxed photographic experience.
Choose a photographer with a regularly updated website as this shows they are working and active. If the photographers portfolio is small then I would suggest you ask to see further examples of work as anyone can buy a camera, shoot a wedding, and find a few good shots in a few thousand. Look for a large body of consistent work.
Make sure the photographer you choose is actually the photographer who will be photographing your wedding as some studios use multiple photographers and send who is available on the day. All photographers have a different eye and style so this might lead to you getting a different result to the one you originally chose.
You need to trust and believe in your photographer to allow them to do their job. If the discussions prior to the booking are difficult and I get a sense that you don’t fully trust me or believe in my ability to photograph your event then I will most likely suggest that you find another photographer with whom you do feel 100% comfortable as this is very important in order to get good results. I want you to get the best photos possible and it doesn’t matter whether they are mine or someone elses.
Beyond the fact that you are getting married the most important thing is the photos. After all as the cliché says “when the music has stopped and the flowers have wilted the only things left are memories and photos”.