First and most importantly, when talking to a potential web designer, take special note about how much they want to know & understand about your business. This is a good first indicator of what type of partner they will be in the project.
If they try to close the sale too hard and fast without trying to understand your business, the chances are they will offer very little value to your business. Only a designer that wants to know and understand you, your business and ethos will be able to represent your true business values through a web site.
Ask your web designers for a structured process on how they develop a site, clearly detailing every design phase. It will show you how organized they are. Here they should be giving you opportunity for input every step along the way, otherwise how could they build the site to be an accurate representation of your vision for your company web site?