this might sound a daft question, but why do you want a fence as opposed to a hedge? If you need some sort of dog-proof boundary, for example, you could have some stock netting + associated posts. The beech would soon grow through the netting and would look good all year round. I have done this with a hawthorn hedge and now the posts/netting are hidden by the hedge itself. Stock netting is made from strong galvanised wire in squares & rectangles & is about 3ft high. I can't remember how many yards/metres you get per roll. I think it was designed to stop lambs escaping, & the way to fix it is so that the edge with the rectangles goes at ground level, with the edge with the squares (which are larger) at the top. I know this sounds confusing, but the idea is that small animals can't get through easily - though cats & rabbits can. I suppose very tiny/small toy dogs could too, but something like a Jack Russell terrier couldn't.
You could put solid fence panels if you want to, but the "downside" of this may well be that the hedge gets less rainwater and less sunshine, and may grow more slowly as a result. Another problem might be that when you paint/creosote the fence panels, the paint could affect the growth as well - creosote almost certainly would.
As with any new-ish hedge, it's important to see it doesn't dry out (no prob this past year!) and to use something in the way of fertiliser & mulch at least once a year, which will encourage growth. My favourite hedge is a mix of beech & holly - looks really good all year round.