Looks like you need some sort of privacy screen between the neighbor also. Think of the entire backyard as a room with the pool just being the main element. Remainder of the space should be filled with items to compliment.

I would have planted larger trees for privacy around backyard, planted grass, clean it and threw everything we do not need.

Start by clearing away the building materials and tools.
Rent a pressure washer and clean the patio, house and area around the pool. Purchase weather resistant lawn furniture to use by the grill, to eat at, and by the pool, to relax. Any areas that need grass sod could be put down. Just water to keep it green. Larger potted palms could be placed on the far side of the pool. Along the perimeter fence plant some evergreen bushes to add privacy. Hope this helps

Some good plants for a hedge to cover the perimeter chainlink. Depending on where you live would depend on the best options. If you need a pool fence upgrading from the chain link would help. You could also consider pool alarms instead of a fence. Sod for the grass and some outdoor furniture and it will look great

Free design consult if your interested let me know your in Tampa.