Disc brake rattle

It's slop between the caliper and caliper mounting pins. The caliper is moving, causing the rattling. My wifes old 2005 Equinox had this problem and sounded terrible. There are some $3 rubber pieces between the pins and caliper to help prevent this. You can replace them like I did on the equinox but they will take a set over time and start rattling again.

Just so happens that my 2012 chev malibu daily driver does the same thing at 25k miles and I'm not too happy about it. It was noticeable starting at 10k and now it sounds like something is going to fall off.

they are called anti-rattlers for disc brakes. readily available most parts stores

You don't say what brand and size vehicle you have but disc brake pads have clips and/or springs to hold them in place. An auto supply store can sell you a kit of new ones. Just be sure that when you install them that you put them in such that they hold the pad in the caliper tight in the direction the braking force would push them against the caliper. If that makes sense.

Can those shims be bought at AutoZone, Advance etc?

You can add shims to the back of the pads.

Or rework the pad clips to make it fit tighter but be careful not to bend the tabs too far or they will break.

Also take a look at the shock mounts and suspension componenets to make sure the rubber bushings haven't broken apart. Or the upper shock bolt hasn't come loose at the frame.