What criteria should I use when selecting an HVAC system cleaning contractor?

You should interview as many local contractors as possible. Ask them to come to your home and perform a system inspection and give you a quote. To narrow down your pool of potential contractors, use the following pre-qualifications:
Make sure the company is a member in good standing of NADCA.
See if the company has been in business long enough to have adequate experience.
Get proof that the company is properly licensed and adequately insured.
Verify that the company is certified by NADCA to perform HVAC system cleaning.
Make sure that the company is going to clean and visually inspect all of the air ducts and related system components.
Ask if the company has the right equipment to effectively perform cleaning, and if the company has done work in homes similar to yours.
Get references from neighbors if possible.
You can also use the Homeowner’s Guide to Air Duct Cleaning as part of the contractor selection process.