Looking at various video clips on youtube, and reading a few sites and reviews, I’ve chosen the Ephrem’s bottle cutter, which is the horizontal type. It certainly appeared to have the most easily controlled and stable action compared to the vertical plastic one and the bottleneck suspended ones. Both hands are free to firmly apply pressure and rotate the bottle easily. The website itself shows the method clearer than I could describe:
Overall, on first impressions, I’m impressed with the stability and firmness of the base grips, the rotation of the wheels and end stop. This should give the best chance of a clean cutting line.