I am an Assistant Scoutmaster for the Boy Scouts, so I see alot of shirts. Sew them on!! The badges fall off the adhesive. The adhesive is terrible and boys are really hard on their shirts! When the badges fall off it leaves behind this nasty adhesive patch that is just harder to sew through after they fall off. I have always thought they look nicer sewn on anyway.
Here's a tip I found once about sewing patches on: Instead of pinning them in place before sewing, use masking tape to hold badges in place. You can sew right over top of the masking tape and then peel it off after it is sewn. Just sew slowly and you will be fine. Another tip is for the pack numbers on the sleeve: Sew them together before you put them on the shirt, so that it is one larger badge instead of multiple smaller ones. Then sew it on the sleeve. You can do it C.! The last couple of times I sewed on patches I had 20 to do at once. That was after summer camp for my son. He is 13 years old.
By the way use a sewing machine and sew just inside the border with a same color thread. Use a straight stitch not a zig zag.