Congratulations on your new home!* It's best not to plant a tree in the same exact spot where another tree once was growing.* If there is a stump there now it will need to rot, and as it does the soil level could sink.* If it's just a hole and the stump has totally rotted away you might be able to plant a new tree there, but if that tree was diseased it could spread to your new tree as well.* Do you know when and why that tree was removed?
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.