If you inherited a collection from a parent or grandparent, there’s a good chance it’s full of hinges, small gummed strips that fasten a stamp into an album. They were the standard for most of the 20th century, and there’s nothing wrong with having used them.
Here’s the honest tradeoff: a hinge leaves a thin mark on the back of a stamp, even removed carefully, and that mark can meaningfully lower the value of anything you’d call mint or unused. For a used stamp you’re keeping for the picture and the history rather than the grade, that’s rarely a big deal. For anything mint, rare, or genuinely valuable to you, a mount is the better call every time, since it holds the stamp by its edges and touches nothing else.
Our rule of thumb: hinges are fine for filling in a used, common stamp cheaply. Anything you’d hate to see lose value gets a mount. It’s a small decision that makes a real difference over the life of a collection.