On the Internet today, there are many people who call themselves web designers and web design companies. Some people do it for fun, as a hobby or part-time. Web designers that design full-time are the way to go.. Someone who does web design in their part-time tends not to take it as seriously as someone who does it for a living.
Make sure your web designer has some formal training from a recognized school. People who are self taught, although I applaud them for doing it, have relied on the Internet for all their advice, and as you know info online can be inaccurate.
The web design company you choose for your job should have relevant experience. If you would like them to design a e-commerce site, it's wise to choose a web designer who has e-commerce sites in their portfolio.
Your web design company ought to be prepared to submit a proposal for your website project along with a contract. Beware of companies who don't give you a contract. The contract should outline just what the web designer will do and how long it will take, the cost, and what you have agreed to supply. Make sure your contract outlines every possible problem that can happen.