Let me start off by noting that when it comes to choosing a videographer, it should be the same process as choosing your photographer. More often than not brides find themselves waiting longer to choose a videographer which results in them not getting the right one for them. Waiting longer means having even more slim pickings than if it was selected during the first round.
Having video is really important, as important as photo. They're two different products albeit may appear initially to be essentially the same thing. One captures a second in time, the other captures the moment, emotion and the real feeling. One lets you think "oh I remember that one moment" the other puts you right back in the scene. They both have their place, they're both necessary!
Upon getting engaged setting aside budget for photo AND video should be one of the first things you consider. Once you have your budget it is very important to seek what style you are looking for. Back in the day there weren't many options and they all..well, sucked. Now, there are videographers that range from $1,000-over $20,000 from light and airy, to dark and moody, to heavy with the vows and emotional to no vows and more of a fun party feel. Find a company that reflects what you are looking for.
Trust your decision to trust theirs as artists and professionals. Whoever you choose has been doing it for a while (hopefully) and letting go and letting them as artists to do what they do they way that they do it is the best thing you can do that will give you the product that you want from them. This goes from filming on the wedding day all the way through the end during the edit phase. Remember, the best thing is trusting them, if you have concerns ahead of time of not wanting them to be too intrusive, tell them that, because you may find out that is or isn't how they operate and may not be the right fit for you.
Never choose someone and then ask them to film differently than how they present themselves. This means choosing a dark and moody videographer and then saying "I want it to look like this! (insert a clip that's light and airy) Videographers are artists who create their look and are not meant to be treated as if they can do whatever it is that you may want them to do...Warning, anyone who says "okay we can do that" and you don't see examples you probably shouldn't trust.
Ask your photographer for suggestions. It is very important that your photographer and videographer get along well, they will be working side by side the entire day. You never would want that relationship to be stressful if either party is upset at the other. I know some videographers that will not work with certain photographers, and some photographers that absolutely despise videographers.
Ask your planner for suggestions. Planners know who is out there, people maybe you haven't come across that might be just the right fit.
At the end of the day (literally your wedding day) after all the time and energy and more importantly money spent on the wedding, you'll be left with photos, and video. It's easy to get distracted and spend money and time on your place settings, flowers, cake, menu, placecards, dance floor etc none of which will come home with you (okay, maybe the cake) Don't you want to at least invest in something that will preserve those memories and those items and all the feels?
Things I hear A LOT.
The biggest regret a couple has is not having a videographer or not spending enough on a good one.
That the decision to go with video was single handedly THE BEST decision they made...
For something that is either a HUGE REGRET FOR NOT HAVING or their BEST DECISION should be considered a priority in the planning process plain and simple, and remember the age old saying, you get what you pay for.