Either way, ask for a bid once you've explained the scope of your project. And be sure that you both understand exactly what is included. Ask for recommendations. You should review the portfolios of several designers, and receive a few bids, before making a final decision. Buyer Beware Be sure you hire a graphic designer with the appropriate background and experience.
Different mediums require different skills.
And a print designer may not be savvy about such things as the hardware and software requirements and limitations that are part of Web page design. If you want both and can't find it in one designer, you may want to hire a graphic design firm with a team of specialists who can produce cohesive work for a variety of mediums. Especially if you expect to work with a graphic designer on several projects, make sure that your personal styles mesh. Good communication is critical to getting the best work from your designer. This describes the resolution of a a computer screen, printer, or scanner.