GaryS

I agree with Matt. Get into the soil and see what the surface roots look like. I'ts always a problem with taper on trees that big. I'm not much of a cut and chop person for that very reason. I think taper is very important.

It looks like the movement of the trunk, from that angle is that it's pidgon breasted with the movement going towards the back, which is OK. It might make a slanting if you choose a different front, it's hard to tell from the photo.
I wouldn't try to make a broom out of it. Beeches and Hornbeams aren't as vigorous as a Zelkova or Elm. I know from working with them. We have both growing naturually around where I live.

As far as where to cut, I'd study the tree a little more to see which front your going to use.

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GaryS