What direction does the backyard face? Where are you located?

The backyard is on the West side of the house if that's what you mean. I'm in Alabama.

I would want to provide shade for the house and the screened porch, locating a tree west of the porch to eventually shade it. Make sure it is far enough away that at full size it will not overhang the roofline. If there is room, I'd do the same thing on the south side. Can't see what's west of the yard. Is there anything you want/need to screen out?

Place trees for shade first to the west/southwest, next to east southeast of area you want shaded. Plant trees that will grow large at appropriate distance, then place smaller, understory trees closer in, possibly grouped depending on tree size.

The trees you receive from Arbor Day will be about the size of a pencil. You will be able to move them around for a few years as you develop your plans. I hope you will purchase a couple of larger trees at a nursery this spring for more immediate satisfaction.

My neighbor got Arbor Day trees and they were so tin her husband accidentally ran them over with the mower.

TINY!!!