I can't give suggestions for the plants as I don't know anything that grows that fast that I'd recommend. Red Tip Photinias are the only shrub/bush that I've had any experience with that's evergreen and will pretty much grow that fast, and I'm not a big fan of them. But, they did make it through last summer (they've been here YEARS) with maybe monthly watering during the drought.

However, whatever you choose to plant, I would plant them in October. It'll give them time to get their roots established before the heat of summer hits. And I wouldn't expect any significant growth the first year, most big plants seem to spend the first year growing their root system then start growing the above ground part the second year. So, I'd really give any bush three years to grow to your minimum height.

I set out a couple of these perhaps 15 years ago. The one that caught the spray from a lawn sprinkler did fairly well, the other died. These plants got no more than 6 hours of direct light. I do not consider them truly "drought tolerant," probably less than arborvitae. The survivor is now 12-13 ft. tall.

I know of only one rapidly growing, truly "drought tolerant" screening shrub / tree, and that is Japanese ligustrum. Once it gets established, you just can't kill it. Regrettably, it is also highly "invasive," and planting it is nowadays considered a gross crime against nature. Too bad it is so aggressive, because it is quite attractive.

Our evergreen screen uses bamboo, and is fifteen foot high at three years. If you are willing to put in a two foot deep, 80 mil plastic rhizome barrier, bamboo may be an option for you, it's very beautiful. We grow over twenty species on three different properties. You'll have your eight foot plus screen at two years.

Other than that, most recommend that you don't put in a monoculture of the same bushes for a screen, for several reasons. It increases disease pressures, and if one tree or bush happens to die, it looks awkward. They say to use several species, magnolias, red cedars, hollies, etc and plant them in a staggered fashion.

Mackel

A couple of options for your area are the yaupon holly and the evergreen sumac, both of which are evergreen, or even the Texas Rain Sage, which is semi-evergreen.

All of these are moderately fast to fast growers, and are native plants as well, which means that they will be very easy to care for, and that they will have built in drought tolerance.

Evergreen Sumac - http://aggie-horticulture.tamu.edu/ornamentals/nativeshrubs/rhusviren.htm

Yaupon Holly - http://texastreeplanting.tamu.edu/Display_Onetree.aspx?tid=38

Texas Rain Sage - http://aggie-horticulture.tamu.edu/ornamentals/nativeshrubs/leucophyllumfrutes.htm

Thanks to all for the valuable contributions and suggestions. I much appreciate that.
Japanese Ligustrum looks highly invasive. I have these next to the A/C unit. This may be a promising one.
Mackel, I did not quite understand the monoculture. Are you suggesting to have different species of screening plants? When mature, the screen would look odd, I believe. I will try to post some pics of the landscape soon.
In Richardson and Flowermound, I have seen Red Tip Phutonia in hedges about 15ft tall. Thats promising, but looks are bland. I feel Nellie (Illex) Holly is better than RTP.
On the same note, Rhus virens (Sumac) looks more like a tree. I aint sure if we can prune and train it to be a screening shrub of 12-15ft tall. I guess the mature height for Sumac is only 8ft. Pl advise.
Can you pl suggest nurseries which sells these shrubs/ small trees on retail at best prices? I need to screen a fence line for a length of about 80Ft. I am at cross-roads.
Thanks to all of you for valuable inputs.

Evergreen Sumac naturally grows as a large shrub and makes a great hedge. The main caveats I can see to using it are that it needs good drainage and is easily overwatered. Yaupon Holly isn't as drought tolerant but can handle clay soil and extra moisture.

Ty

I tried to upload a few pics on this forum, but in vain. Here is the link.

Here is a link that might be useful: FenceLinePhotos

Wow Aukumar, you've got a lot of space to cover there!
I normally watch the ads for all of my local nurseries in order to see what the best prices are currently, and I find that the Garden Shed usually has the best prices, but I'm not certain that you're in the right area to go to any of those, as they are mostly near Fort Worth, and I'm not sure exactly where you live. If you do live near Fort Worth, you might want to check out Weston Gardens for good advice on what to plant, as their mission is to provide native and naturalized plants that will do well in our climate. I have provided their link below. Good Luck!

Here is a link that might be useful: Weston Gardens