Where are they based?
A web designer doesn’t have to be local to you but it’s usually beneficial to have someone who is based in the same country. Different working hours could cause delays and can be frustrating if there’s a problem with your site.
How long have they been in business?
This is important. You don’t want a web designer that is around one day and gone the next. Can you be sure that if they design your site that they will be there to support you for years to come?
Size of the company
Generally speaking, the size of the company provides you with NO indication of the quality of work they can produce. There are a lot of freelance web designers who can produce far superior work to larger web design companies.
Don’t let your preconceptions about the size of a company get in the way of the facts.