I like to use a modified saddle stitch. I like sewing my pouches inside out to hide and protect the stitches. I then use an awl to make 3-5 stiches every inch. I use hemp linen thread and sew it back and forth in a running stitch the length of the bag. Upon reaching the end you go backwards until you end up where you first began, covering all the unstiched areas with your new stiching.
To save time some use two needles and weave them back and forth, but using one needle is easier for me and I am in no hurry.
Leather is what ever you like. I have used pig skin, cow splits, elk hide and hemp linen canvas with success. I prefer a thicker but soft leather myself like cow, but pig skin really works and wears well. I have even seen a fine groundhog pouch which looked great!
I like to put in small inner pouches before sewing up the bag to hold oil and small tools like my turn screw. I make these from thin hide to simply keep the pouch organized.
Make sure you don't go too large. Most original pouches were small. My rifle pouch is 7" by 7" and my fowler pouch is 8" by 8". One of my first pouches I made 10" by 10" and it was too large and lacked the support. You really don't need to carry much to shoot, and the extra tools can be stored in your haversack. This is simply my preference, of course you need to find what works for you.
Here are some pictures of the stiching to get you started. Good luck and keep up posted on your progress!