Congratulations on your new home!* You don't say what type of hydrangea this is, so it would be impossible to say for certain.* Some are pruned and some aren't, but they all get pruned the year before.
Hydrangea arborescens (Annabelle types) and Hydrangea paniculata (PeeGee types) are pruned in fall, but you might be able to prune it now.* You don't say where you live, so I don't know how long your growing season is.* Keep in mind that if you have a PeeGee type or Annabelle type and prune now, you may end up with canes that will droop too much and you may have to stake them as they wouldn't have had time to fully mature.
Why don't you take a look here to see if that helps.
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.