In my opinion, you typically want to separate the design and development aspects of creating a website when dealing with individuals, versus a firm that can provide the complete package. Design and development require different mindsets and it takes a unique and/or very experienced person to do both parts well (contrary to what many programmers who like to think of themselves as designers may believe!).
I would recommend working with a designer to do the site design and then hand that over to the developers so all they have to do is cut it and skin the website. This allows both parties to focus solely on doing what they do well.
While the saying 'you get what you pay for' basically holds true, that's not to say you can't find a good designer for a bargain price. The web design field is flooded, so newcomers who aren't connected with a firm or group are often forced to work for peanuts until they can build a portfolio up, even if they have the skills and a lot of talent.
The best way to find these up-and-coming designers is to simply go to the places where they showcase their work with fellow designers. I'd recommend starting with Abduzeedo, Dribble, Logopond, and the web section of deviantART. Look for a designer who has a style you like, check out their additional work on their personal website, and then drop them a line. Chances are they're not going to have any Nikes or Microsofts in their portfolio, so you should be able to hire them for an affordable price.