A cheap panel antenna mounted outside the building in the order of 7-12dBi gain would do the trick nicely. Just check the spread on any antenna you consider buying to make sure the angle is wide enough to cover the entire area.
It is hard to say whether the single tree will present a problem as it depends on its size and foliage. Noodles pointed out a few good points on this.
Once you have an antenna, its often a good idea to mount it in several locations and see how performance is affected by using a laptop running
Netstumbler or similar to check the strength.