Check their work
Ask to see examples of their work - not just fancy front pages, but active web sites so you can check how quickly they load and how easy they are to use. Try to view the sites as a potential reader or customer, not as a website owner.
Watch the price
A professional web designer will talk to you, define your needs and give you a fixed quote. The quotes you get will vary - price is not always a clue to quality. Be careful of hourly rates because, without a set target, the hours can just stretch on forever (which is a good reason not to let your staff do it)
The other side to this is that you must play your part. If you are too vague about what you want, they can't be expected to give you an accurate quote.
Integration into your business
A web site needs to fit in with the way you do business, the way your customers do business, and the way the Internet works. Professional web designers consider these things before they even begin to think about the colour and layout of web pages. They will also be able to advise you about issues like copyright and security.
Gaining and keeping an audience
Developing strategies to get your customers to look at your web site and giving them a reason to return is a hidden part of the web designer's task.
Integration into the web
Your web site is part of the big web. Ask web designers how they are going to encourage and facilitate links to your web pages from other web sites.
Adding an affiliate program
Affiliate marketing can be a cost-effective way to promote your site. It is usually better to use a network service rather than having an in-house system. If you plan to use affiliate marketing, you should discuss this with your web develop right from the beginning of the project. You'll find more on affililate marketing here
Measure your success
Ask your web developer about the sort of statistics you can get to monitor the performance of your web site.