Tagging guns are not all created equal. The gun with the shortest tacks is the MicroStitch gun by Avery Dennison. I purchased one several years ago and use it regularly. The tags are short enough to keep the layers from shifting. The guns at Joann's don't work nearly aws well as this gun. I've used them both. The gun came with a glass heart, about 3/4" thick and square. You slide the heart on the table below the area where you want to insert a tag. The heart holds the fabric sandwich up off the table and allows the gun needle to be inserted through all the layers of the quilt, installing the tag without damaging the surface underneath. The little tags are about 1/4" long, the gun needle makes a small hole and the tag is easily removed by clipping.
Using this little gun is so much faster than basting or safety pinning.
Amazon.com sells the gun for about $27. Just do a Google search for "microstitch gun" and you'll find places where you can buy them.