I would NOT tell the neighbor that I now have a gun and will use it. The less they know about that, the better. What if another neighbor shoots her dog and she says you did it? Shhh. My advice is, in addition to all else you are doing and have been advised to do, go to a neighbor that you are friendly with and get them to teach you firearm safety and how to use it. A single shot .22 will manage your problem and be fairly safe, but you need to be comfortable with handling it. Then, practice, practice, practice. There are so many folks out there willing to help you learn! Swing by a rifle range on a Saturday morning and talk to the folks shooting, someone will help you and you'll have a new friend. BTW, i let a 10 year old shoot squirrels in my orchard (yes, he ate them) and now he's in his 30's and brings me venison--what goes around comes around.