I can see one or two ornamental trees by the garage on the left side of the house. They would also help providing shade.

"We know our first priority is probably redoing our back deck but we are unsure if we should keep the same shape." You're there using it and we're not. What are the shape/size dissatisfactions with the deck that you've acquired? At least it looks finished so I don't know if I'd make it the first project. IMO, what makes your yard seem lacking is the lack of landscaping. There's no "foundation" planting around the house. and the yard perimeter planting seems incomplete. The trees are nice but it would look a lot nicer to have a "lawn" of groundcover below them, as opposed to a sparse, dying turf area. Turf is only going to do well where there is adequate light. At minimum, it should be solid, weed-free mulch. But eventually, you'll want groundcover so you don't need to be replenishing mulch on a periodic basis.