Check out yellow or orange cestrum. Grows fast, ever-green, bushy, mine are about 8 or 9 ft tall, blooms continually except in winter. It makes a great hedge.

Cestrum 'orange peel'

Google Images

Glossy abelias would be nice too.

I thought ligustrums were considered invasive, but I will look into that. Thanks!

The cestrums are very pretty!

Here is something else you might consider for the chain link fence while the hedge is growing. We got permission from our neighbors. They loved the idea:

Look what we did with our chain link fence. It's been five years. Things have sure grown since then.

Incidentally, the plastic ties we used to attach it held. Only a few popped off last summer.

Yes, I've contemplated many times doing something like that. Many people in our neighborhood are converting to privacy fences, but we have a large yard and I just can't justify the cost. Plus we really do enjoy being able to talk to all of our neighbors over the fence. I'll look into something like that.

If you do vines, make sure it's not one that will bring the fence down. My neighbors planted wisteria all along their chain link fence and last year noticed that the vine is bending the fence down. Right now they have it propped with some wood posts, but hopefully they will do something a little more permanent and a little more attractive.

And yes, ligustrum is on the invasive list.

A very clever fairly inexpensive privacy screen solution using annual vines followed by perennials was recently posted with a photo on the GW Landscape Design forum. It's Yardvaark's first response in this thread - Wanted: Fast Growing Privacy Screen.

Can think of a number of vines that might work well with this in Texas depending upon the amount of light.

Wax Myrtle hands down

Photinias are getting a thumbs down by many reputable landscapers

Yep, they're very susceptible to black spot.

Lady Banks Rose would be/is perfect. Ours was a mere bundle of twig ten years ago and now she is 25' wide and 20 feet tall! What neighbors? She will also stay mainly evergreen...

Oh my gosh! I planted a lady banks this year, I had no idea they could get that large. Ok, I'll keep that in mind. They're neighbors to the South, so it gets a lot of sun.

Lady Banks rose is beautiful, thornless, huge and graceful, but you've got to have, and be willing to devote, a lot of room for it. It is literally a 'house eater'. My son in law planted one along his back patio and in a very few years it was hanging over the front porch ... LOL. You can imagine what a chore it was to remove.

In my mother in law's hill country, rocky, practically soil less two acre plot it took over about a sixth of an acre, maybe more, growing up through the oak trees. It was gorgeous during it's two week bloom time and very graceful other times -- if you like the jungle look, which I do, but it gets too big for my yard.

You who have Lady Banks -- how do you manage its size? Or maybe that should be a subject for another thread.

I'm curious how to handle it too. I planted it against the fence and am now questioning whether that was a good idea, haha.