If it were me, I'd stick with someone who does nothing but build decks, as opposed to a general contractor or handyman-type. Reason being that they will have figured out what works and what doesn't. And do some serious research before you shop for contractors, so you are aware of materials and techniques that are out there.
Another thought--why not go down to a local lumber supply place (one that sells a lot of deck material), and ask one of the sales guys who their biggest deck supplies customers are? Then contact several of them to chat about their work product. Ask them if their decks meet all local building code requirements, and also if they conform to the IRC requirements. Also, ask if they will provide you with a working drawing of what they propose to build before any money changes hands, or if they just work from a vague plan in their head (that you may or may not be happy with in the end). Bonus points for any prospective bidder that subscribes to Fine Homebuilding magazine (past issues have included quite a few articles on good deck building practices).