Silver birch is lovely but won't screen him out - you need evergreen for that really. There are some good ones, Thuja for example, better behaved than ye olde Leyland conifer. Or holly, but it grows slowly.
I take it you've ruled out a viewing platform and charging people to come and watch the guy 
We just put in about 15 trees, garden slightly smaller than yours - it didn't cost a lot as we went for 'clearance' ones and we have a brilliant, very long standing nursery near here that has thousands of enormous trees, very reasonable prices - talking around £20-25 for most of them, and they are already about 10ft tall.
I got two birch, an elm, two crabapple, cherry, apple, pear, walnut (lovely), cercis (that one was very expensive though!), Chinese hawthorn, normal hawthorn, plum...the more the merrier!
Also there are a lot of whitebeam trees round here, they are stunning at this time of year though like most deciduous, won't provide winter screening.