The cheapest way to mail magazines through USPS is Periodicals, a mail class built for magazines, newspapers, and newsletters. It only pays off in bulk, and you have to apply for the mailing privilege first with Form 3500. If you're sending a handful of copies, skip Periodicals and use Ground Advantage or Priority Mail instead.
Periodicals is a discounted class for publishers who mail the same title on a regular schedule to a real subscriber or requester list. The discount is real, but USPS expects volume, so it's built for a print run going out to hundreds of readers at once, not a one-off.
If you mail magazines regularly and in bulk, Periodicals is the cheapest option and worth the setup. If your volume is small or occasional, the qualification requirements and per-mailing minimums won't pay off. In that case a single copy ships fine on Ground Advantage or Priority Mail, priced by weight and distance.
Once the account is set up, you can repeat the process on whatever schedule your subscription cycle runs.