The style of photos you are trying to achieve will be a big determining factor in choosing a wedding photographer. Every photographer has their own image and take on how wedding photos should look, you will need to make sure their take is compatible with yours.
You should ask to see a few full wedding photo albums to get a sense of what images they produce and how they tie the photos together to capture the overall day. Just going off one image may not give you adequate information to make a choice. It may turn out that every photo they take looks the same or they have trouble weaving the story of the day in photos.
This will depend on your entire wedding budget. Keep in mind that there are expenses involved in running a business and a photographer needs to cover these costs and also pay themselves so try to set aside a reasonable amount to keep your options open.
Once you know your wedding date you should book a photographer in. Some popular wedding photographers can book out an extreme amount of time in advance so bear that in mind.
Depending on what photo package your photographer offers this may involve getting a wedding album with some enlargements or could be entirely digitally delivered.