I'll throw out a few thoughts. If the bag is going to be stitched inside out, so that the stitches end up inside the bag, probably doesn't matter that much how you do it. The over stitch wheel creates a very modern, evenly spaced stitching and sometimes that's what you want however sometimes a less than perfect stitch spacing looks more rustic.
An awl more or less pushes aside the leather to create a hole. Don't use a "paper punch" that actually punches out plugs of leather. The chisels will cut the leather but they are really used for lace, not thread.
Linen thread is pc and stronger than cotton and you can buy 100% linen thread at Joann Fabric for $2 or so. Get off white or natural.
Here's a good trick: if you use an awl the holes will want to close back up. In soft leathers the holes can disappear. I use tiny brads and as soon as I make a hole in both sides of the leather I'll insert the brad. You end up with a pretty weird looking project but after all the holes are made and filled with brads I'll start the stitches, pulling out a brad at a time and immediately running the needle into the hole. I use a very long thread with a needle on both ends and start with the middle of the thread in the first hole and then on the next hole a needle goes through that from either side- like lacing up a pair of shoes. At the end of the seam don't knot the thread, just back stitch 3 holes and it will hold. On a knife sheath I'll back stitch one thread end three holes and the other 2 1/2 or 3 1/2 holes so the cut off ends are both on the back side of the sheath.
So, get some linen thread, an awl, a small pack of brads, and a couple of heavy needles. The shoe lace method wears the thread so you might want to get some beeswax and rub that over the thread from time to time. If the leather is thick, maybe a pair of pliers to pull a needle through a tight hole.
When you get into the multiple layers of leather, such as a sheath with a welt, you might want to glue the seam to hold everything in place and then stitch it.