A better question is: what trees will grow best in your climate and location, that will not have invasive or damaging root systems, and that will have minimal shedding of leaves. Evergreens might satisfy that last requirement, but keep in mind that they do still shed needles and sometimes branches if it is windy enough. But it's a moot point if you don't plant the kind of evergreen that is suitable to your climate and the location.

So first you need to find out what trees are suited to your climate, and of those what are suitable for planting near structures. A good local nursery (not Home Depot or Lowes) will be able to at least steer you in the right direction. Another option would be a landcape architect, a Master Gardener if you have active in your area, an arborist, a reputable pool installation company that has done a lot of work in the area, etc.