If you're looking for design, make sure you have good chemistry with the designer - because you need to like the final product, and it may take many iterations. This can occupy a huge amount of time.
However, looking for a designer is only half the work - you also need to get the design functioning. Some designers have programmers who they work with, or can refer you to. If the complexity of your site is high, then you may want to start by looking for a development firm who can refer you to graphic artists.
There are sites, such as 99designs, which facilitate the finding of graphic artists. I don't have personal experience with such sites, but have heard stories of good and bad results from those services, so it may be worth investigating.
There's also word-of-mouth. For example, depending on your project, I may be able to recommend a firm specific to your needs (feel free to get in touch directly). Other people in your network may be able to make recommendations.
It's hard to benchmark pricing - quality and speed can affect this, as can the local market, as well as how clearly you've defined the requirements. Prices will vary significantly between companies.