since you're not concerned with "going fast" and you want stable control on downhill for hard, mixed surfaces, I'd look for a "fitness hybrid" or something like a touring/ gravel bike. flat handle bar, not a drop bar. drop bars, IME, are great for aerodynamics and for moving your hands around to different positions for longer rides. I don't think you'll get much out of that and it won't be worth getting used to what most people consider un-intuitive controls on a drop-bar bike.
conventional road bikes have narrow tires that need high pressure. that's going to most likely not be fun for you when you leave smooth, paved roads. look for something with at least a 32mm tire. the size of the tire will be limited by clearance in the frame and fork, and conventional road tires are 23–28mm, with a trend growing toward wider tires.