Congratulations on your new home!!* I think what you have is a Lady's Mantle aka Alchemilla mollis.* Does water form beads on the leaves?* I did a google for this plant and it appears to be the top row, second from the right.
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.