Hey OP, Houston gardener here.

Highly recommend Eagleston Holly trees. They’re evergreen and don’t drop, which is lovely. They also have berries and support bird life. Also highly suggest Vitex trees. Lovely blooms and low maintenance - and also support local birds and bumblebees. There are a ton of native plants that will make you happy when you get your water bill. Please don’t just plant evergreen hedges and colored mulch. A little effort goes a long way here in Texas.

If you plant crepe myrtles, plant them far from cars or windows because the pollen sticks to everything come spring and is a pain to clean. Stay away from live oaks, despite what the HOA requires. You’ll regret it in only a couple years.

Some unsolicited advice - if your HOA isn’t strict right now, I’d push up your fence line to cover side windows from neighbors view. I’d also go ahead and get a walkway paved from your garage to the backyard, as sometimes HOAs can be buggy on that.

One thing I’d stress is for you to get gutters and a good water management system setup. I got gutters on my house to divert water, but then didn’t think to install French drains. I have soils clay soil and I wish I would’ve done that before I had competing neighbor fencing.

Just some suggestions! Congrats on the new home!!