When I used to shave, rotary shavers chewed my face up the least, while foil shavers (what you have) and razors completely turned my face to hamburger, instead of partly. A basic Norelco corded triple-head was my go-to, and I kept it clean. This said, I wouldn't have called it a "close" shave. Smooth (excuse the skin damage), but not close. Eventually, I just embraced the beard, and my skin finally just stopped being angry, and the closest I get to shaving anymore is running the 2" Wahl clippers across my face without any clipper guards along the beard edges, which is at its best, leaving an aggressive 5 o'clock shadow in its wake.
If your skin doesn't like being shaved bare, the best and easiest solution is to let hair be hair if at all possible, even if you embrace nothing more than a CW drama 48 hour beard.
This said, if your current razor isn't giving you serious problems and you actually want to be clean shaven? Don't mess with what's already working.