Well, I make it over to FW periodically so I hope it's okay for a Dallas guy to reply to your post.
I'll leave the location to the local experts but, personally, I don't like the near east side or south/east along the 287/35W corridors. West side or far south/west seem to be a little less on the "creepy" scale.
Gated vs. non-gated isn't a big issue from my perspective but I know some of the ladies feel a bit more secure having a little better traffic control and that one last checkpoint before giving someone the green light in.
I'm cool with animals as long as they are not racing all over the bed and the place doesn't reek of, well, certain animal odors.
And, while pets can make a place seem a bit homey, so do pleasant furnishings and a gentle touch.
I probably look more for comfy than homey. A place to shower, a clean towel, fresh linens, a place that isn't littered with junk or trash, attentive attitude. Those are some of the things that make for a pleasant experience, IMO.
I'd be glad to give you some more observations at any time. Maybe even in person at some point.
Good luck with your search for a new place to call home.