Yeah let’s talk beech! Bonsai4me used to have a great article on beech pruning, but it’s no longer connected to the species guide. The big thing with beech pruning is that you MUST leave a bud on the branch- you can prune back hard, but if you don’t leave at least one bud, it will drop the branch entirely. In my experience, if I leave two buds behind, the tree will push a lot of new growth at the farthest bud from the trunk on the branch, so I really cut back hard. If you don’t, you get great budding on the branch tip, but then have to wait an entire year to cut back again- lots of time and energy wasted. I also usually only prune them back hard in late winter for this reason- if it’s a very cold year, I can expect slight dieback of some branch tips. If I cut back hard, there’s a chance that the one bud I leave will die off, meaning I lose the branch. By waiting until the threat of very cold weather has passed, I can selectively prune with relative safety. It’s similar to what I do with hackberry.
The two best things about mature beech are the silvery, smooth bark and the golden leaves in the fall. I feel that beech are suited to either an informal broom or informal upright, but still with a mostly straight trunk. At least where I am, beech dominated forests have grand, nature trees with spreading canopies and well defined foliage pads in lower branches. You don’t have to have a fat, squat trunk to make a nice tree- in fact, you can achieve a good look with a somewhat thinner trunk, you just have to have an appropriate and slightly larger size.
I don’t know how much space you have, but I would put that tree in a 5 gallon pot or larger, and place it on a tile or piece of wood for the nebari. Personally, I would wire that left leader into a more vertical position so you don’t end up with a slingshot look, and let the tree grow for a few years, increasing the finished height by maybe a foot. Then start pruning it back hard to increase the number of branches to fill in the voids and ramification. I think you could end up with a reasonably realistic tree in a few years.
Option b- cut that tree back to the second branch (currently angled to the left), wire that as the new vertical leader, and then let it grow for a few years. That may be more reasonable, if slightly slower, to get rid of that big area devoid of branches in the middle trunk. Now that I really look at it, that’s what I’d do. Plus, the first right branch will be in a good position to be wired, and it will be the thickest- otherwise, you might end up with a thin first branch and thicker ones above.