If you want to do it right, you want a bar tacker sewing machine.
Juki is a name brand model, but you can get Chinese knockoffs for lesser costs, and as they are only sewing simple labels onto garments I don't really see much going wrong.
However you can just use a standard sewing machine.
We don't currently have a bar tacker, so we spray tack the back of the labels and sew them with standard sewing machine.
We also sew them in the necks rather than on the hems, the shirts have to be unsewn, the tag inserted, and sewn back together, this is a bear, don't offer it
But on the hems, sleeves, bartacker is the way to go, or a standard machine will do but much lesser throughput.