Lots of photographers (myself included) do a mixture of these, but there are some photographers who will only really do one or the other, so be careful when you book. If you want fabulous bridal portraits you may be disappointed if you hired a reportage photographer. Likewise, if you want special candid moments you might not want to choose a more traditional photographer.
What type of person are they?
This is one you might miss, but it can have an impact. If you're a very energetic group then a photographer who is quite low-key and reserved might struggle to provide what you're looking for. On the other hand, if your group is quite restrained and conservative, a photographer who's the human equivalent of a bouncy ball might grate on you.
This one is only particularly useful if you met the photographer at a wedding fair; it's hard to tell someone's personality solely through text on a website, so bear that in mind.
Are they equipped for what I'm asking of them?
Wedding photography is a tough field to work in, and while I'm definitely not interested in being a gear prescriptivist, there are a few things you should look out for. Their main work camera ought to be a DSLR or a Mirrorless camera with interchangeable lenses. There are of course other cameras that fall outside of this particular rule (Fuji X100's, for example).
They should realistically have two DSLRs, or a DSLR and a mirrorless/high end compact as a back-up. If their camera goes kaput during your wedding if they don't have something to fall back on, you'll get no pictures and be rather peeved. It doesn't happen often, but why take that chance?
If you want portraits with off-camera lighting you should ask them whether they're capable of providing that before it comes to the big day.