Just a quick word about getting goats/livestock to keep with your birds. I started my farmer life with American Blackbelly sheep as my first flock (to control the tenacious grass in our pasture), and while I thought I was merely going to use them as lawnmowers, I did my research and could now probably teach animal husbandry at a university somewhere...there is a TON of information you need to know and prepare yourself for before you get sheep or goats or llamas or whatever. They are NOT low-maintenance animals, I don't care what breed you choose...just like with poultry, if you're gonna raise healthy animals, you need need need to do tons of research and just educate yourself. on what they need. (I started raising chickens and ducks and turkeys to provide pest control for the sake of the sheep's health, actually...and then I got to find out all about the poultry needed for good health, too!)
To your predator issue: I've seen my neighbors lose chickens and baby turkeys to snakes, possums, and hawks, but so far (knock on wood) MY chickens, ducks, and turkeys have been spared. I keep my flocks out in the pasture all day unsupervised (I have to free-range them, because I use them to control the bugs in my pasture to keep my sheep healthy), but they stick close to the sheep most of the time...maybe the sheep look scary to predators, I don't know. My turkeys are also very large bodies in the pasture, maybe they help as well. I also have several large trees in my yards and pasture, they probably provide some cover too.
Personally, I vote for you to try a rooster. If you have plenty of open space for him to escape from the hens, then he probably won't get bullied or cannibalized by your hens, but that depends how territorial your hens are. When my rooster showed up in my yard out of the blue, he was a baby, and somehow he fit right in with my mean girls and they shared the pasture together no problem. I didn't have a choice in breed, since he adopted me, but he's a medium sized reddish guy with a big green tail...he looks like a mini RIR roo. I've found the gentler-sounding crowers tend to be the medium-to-large sized boys, surprisingly...my mid-sized rooster has the cutest little croon, and my neighbor's huge RIR roo has a deep throaty crow that is very gently and quiet...however, my other neighbor's tiny little Millie D'Uccle rooster has the most obnoxious, screechy crow you've ever heard. Or maybe you should get a big tom turkey who can strut around your yard like mine do, he'd keep everybody safe
Good luck...