When it comes to choosing a web designer, you need to establish what is important to you. It may be that price is the main factor and you want something for as cheap as possible, or it may be that money is not really the main concern and quality and speed are most important.
Once you have a rough idea of what you want to accomplish with your website you can start to obtain quotes from web designers. Some designers will design and program a website others will only design it in which case you would need to find a programmer too. Ideally you want to use a company or individual that can offer both otherwise you may have issues with communication between the two.
Be wary of always going with the cheapest quote you have as you may find that quality suffers because of it. Always ask to see working examples of work they have created and possibly even to speak to some of their past or current clients to get a review.