Myself, I would consider a 1 inch diameter trunk too small a caliper for styling a beech. If it were mine I would move it to a grow out container. I would construct a box that holds at least 5 gallons of potting media, but is wide and only 4 or 5 inches in depth. Cut off of a 55 gallon drum, or a box 24 x 24 x 4 inches or 36 x 36 x 5 inches or something similar. Pot the beech in there and let it grow for 3 years.
In my opinion, the beauty of a beech is the smooth bark of the trunk. I would as much as possible grow without chopping or only chopping on one side of the tree (diagonal cuts) so that the front of the tree is an image of smooth, unblemished gray bark. A carelessly chopped beech will look awful.
Do look at articles about European Beech by Walter Pall.
American beech has larger leaves, and is slightly more difficult to work with. It is more "single flush" than European beech and it does not bud back as easily as European beech.