1. Their overall aesthetic, brand, and style
Does their website catch your eye? Does it display their best work? Are they active on social media? I always recommend exploring not only a photographer's website, but also their Instagram and Facebook pages to see more examples of their work. High-end wedding photographers are extremely selective about the images they post on Instagram and will carefully curate their feed so that everything is pleasing to the eye and is the best representation of their brand.
I also recommend asking to see a full gallery of a wedding a photographer has shot at your venue, or at least a full gallery at a venue of a similar style and feel. This will give you a better idea of how their aesthetic will suit your venue. For example, I love working with natural light, film photographers for semi-outdoor weddings because they know how to capture the lighting juuust right, but not all natural light photographers are as familiar shooting and lighting up an indoor ballroom for your reception photos.
2. The way couples look and are posed in their photos
As a bride, you will definitely want your photos to reflect the hours and hours you spent getting ready and choosing the perfect dress - this is the day where you will look and feel your best, ever. Does your photographer know how to shoot in flattering lighting so that your skin is absolutely glowing and not orange or shiny? Also, do the portraits of couples look natural and not 80s-style-prom-posed? (I mean, nothing wrong with a few staged poses, but there are so many beautiful examples of more delicate poses!)
A real example: my husband and I worked with Love by Serena for our engagement photos back in 2011. Half of our shoot took place in a field on a too-humid October evening, where we were sweating like crazy and getting eaten alive by mosquitoes. I was honestly horrified that our photos would show every bead of sweat and red bite on our arms and legs, but when they came back it looked like a romantic perfect-weather day with zero bugs and not a care in the world.
A talented photographer will make you (and your wedding) look magazine-perfect.
3. Film vs. Digital, and Lighting
This point loops back to my previous two points but is also worth considering! Film photography is incredibly popular right now, and for a reason. For outdoor photos during "golden hour," (the time right before sunset!) film captures and plays with lighting and scenery in an etherial way that digital images can't fully replicate. Film also does magical things with tulle (that gauzy, light, wedding dress material) and movement. Everything seems a bit more delicate and natural - like you are looking back on an image in real time.
Digital photography has perks as well, as it is wonderful for indoor, low-light locations and is a more cost-effective option. However, I've found that sometimes the eye and experience of digital-only photographers can vary widely, so please, please do your research and make sure your digital-only photog is completely awesome and edits their photos in a filter and style you like before booking!
4. Do they specialize in weddings?
I tend to prefer to work with photographers who truly specialize in weddings or only shoot weddings for their profession. Although a larger company's promo photos may have acceptable composition and coloring, someone who is constantly working at weddings will be the most tuned in to every little moment happening on your day. Wedding-only photographers also truly love weddings. I've found that they are sensitive, romantic, observant, intuitive people who will seek out the smallest private glance between the bride and groom when no one else is looking. They'll capture your relationship on camera with true thoughtfulness and meaning - and your photos will show it.
5. Their responsiveness and personality
Do they respond to emails promptly? (Meaning, within 24-48 hours on weekdays!) Do you actually like them as a person? Do you get along easily and look forward to chatting with them? Aside from your wedding planner, your photographer(s) will be the people you see and communicate with most on your wedding day, so it is definitely important to feel comfortable, at ease, and to be excited to spend time with them! Overall, I advise my couples to book a photographer whom they respect and trust.
For me, the photographer is perhaps the most important vendor you'll invest in for your wedding day because your wedding photos will last forever. Working with a strong, talented, intuitive photographer will elevate the work of your other vendors and will be a meaningful wedding investment that keeps on giving for years and generations to come.