Peruse the magazine racks at bookstores. Bookstores typically have a wider selection of periodicals than grocery or convenience stores. Page through a few magazines that have the words "family" or "parent" in the title. If you find one you like, buy it, or remove one of the subscription cards that accompany the magazine. These are usually tucked into the magazine for readers to take and fill out. Subscription prices are usually less than the shelf price.
If you want to subscribe to a family magazine and want some of your payment to go to a good cause, check with your local elementary, middle or high school. Many schools have fundraisers that include magazine subscription sales.
The most budget-friendly option for finding family magazines is through your local library or thrift store. Many libraries have a small bookstore where they sell recent copies of magazines for a fraction of the new-magazine price. This is a smart and economical way to find out if you like a magazine enough to pay for your own subscription.
Look online at web versions of family magazines. Enter "family magazine" into your search window and click on the first few options with titles and descriptions that you like. You will have access -- although it might be limited access -- to articles, images and ads.