Before calling any website design companies / designers. You should have a budget in mind. It's like buying a car. If you have $15,000 budget, then you should be thinking of buying a Toyolta Corolla. On the other hand if you have $50,000, then a Mercedes is what you should think about.
A website can cost anywhere from $300 to $50,000 depending on what you are asking for. Have your budget ready when asked. Some website design companies only work with budget over $2,000 or $10,000 or $30,000. There are always some companies that works within your budget. Therefore, call at least 6 companies. Then from the 6, select 2 or 3 that can work within your budget. Then you can select the company that you think is best. But how do you know which one is best.
In order to answer that you need to know what you are looking for. Building a successful website requires many technology. In the website design industries, many companies specializes in many different technology.
If you want high quality flashy website that doesn't required search engine optimization. Then should choose a company that specialize in Flash and animation.
If you would like a simple brochure website that people can be able to find on search engines. Then you should choose company that specialized in search engine optimization.
If you would like to sell many products online and need a lot of visitor from the search engines. Then you should choose a company that only one specialize in search engine optimization but also database and ecommerce integration.
There it is very imporant to ask the website design company what they specialize in.