Like Ken, I was taught to sharpen my straight-razor lying flat on the stone. The only stone I ever used was the ultra-fine (mirror finish) ceramic razor hone I bought with the razor (and got the sharpening and use instruction for free). This was back in the ’70s.
If you maintain a razor well, the ultra-fine is all you’ll ever need, aside from a traditional barber’s strop and a shaving brush.
Hands have gotten too unsteady for putting that kind of steel to my throat anymore, so the razor and strop are wall-hangers.