How do you choose the right production company?
Once you've found a prospective production company, talk to them!
Do they tell you what they think of the project, do they share their ideas with you, or are they happy to just go along with your suggestions?
What work have they done before? Ask them for their show reel and check out their website to find out if the company has a good track record. Find out if their past clients are happy with their work. Even better, find out if they were ecstatic with the results.
Talk to their previous clients and find out how well they worked together - recommendations are always a good sign of professional and reliable work. Find out why they chose that specific company, and if they still use them for ongoing business.
Also, trust the production company. The producer/director will have a clear idea of how the edit and finished production are going to look. Discuss their vision with them.
If you don't understand the production procedures at any time in the process, ask and they should be able to explain everything to you. If they can't, then they probably shouldn't be working for you.
Also don't take "can't" as an answer! A good production company should want something that not only gets the job done, but also something that reflects their talent and makes you look good.
Finally, if you ever feel the project is not going in the right direction, don't hesitate to say something! Ask for alternative ways and ideas. You are the client and you are paying for it, after all.