Congratulations, and YES!... Definitely use a clean needle and syringe for each injection! I generally inject in the thigh, but sometimes the deltoid or glutes. It can be a little hard to reach around to the backside for many people, so the thigh remains a more common site. I used to have a very methodical rotation of sites, but after a few years, ...eh, I just do what seems easiest on that particular day. I have never looked into subQ for myself, nor has my doc mentioned it, but I know there are quite a few people who do that.
Quite frankly, I would use a gel now if I could afford it, as I am very tired of giving myself shots!