Proper and consistent soil sampling is a must in order to reduce inconsistencies and get the most accurate results possible.

Proper: When digging the samples, use only high quality steel
tools. Use only plastic buckets for holding and mixing the samples.
Avoid brass, galvanized or other zinc coated utensils. Otherwise, the
sample can be contaminated. If you do not have a soil sampling tool
(auger or
probe), insure that your soil sample is an even thickness vertical slice
and not a wedge shaped slice. Take 8 samples, evenly
dispersed, from each 60 x 60' area. Try not to sample any sooner than 30
-60 days after an amendment application.

Consistent: Take all samples to the same depth (4" for turf)
and do so each year of testing. Use the same "range" of soil for each
sample and from year to year. e.g. soil from the 0" depth down to the 4"
depth (preferred, but remove the soil surface and any fresh fertilizer
prills it may contain). or from 1"-4", or the 2" to 4" depth, etc. Stay
consistent. Take the samples in the same
month each year.

Use the same lab each year. Use an established professional or
university lab that offers a broad menu of testing processes, reports
results in ppm or lbs/acre and at a minimum, reports CEC/TEC, Ca, Mg, P,
S, K, Na, OM, Mn, Zn and Cu. Verify that they offer ammonium acetate
cation and buffer pH testing and that their fees are reasonable. Verify
if they use Mehlich III as their default extractant and extra points if
they offer Bray and Olsen too.

Do the vinegar test on a small sample. If it fizzes, request that an
ammonium acetate test be performed. If it doesn't fizz, either ask for
or be prepared to request that (if the test comes back with a soil pH
less than 6) a buffer pH test be done.

I would encourage you to read this whole thread for additional information:

http://forums2.gardenweb.com/discussions/4535255/taking-soil-samples-for-lab-analysis-get-your-moneys-worth?n=14

That looks more like gravelly sand than clay.

Where do you live?

What are you going to use the lawn area for? (kids playing, pets, just to look at, etc.)

Is there much shade?

Just for looks basically, maybe some out door parties but nothing serious. Yes there is shade 4 pecan trees and I live in South Georgia.

With the location, shade and soil conditions, I would be looking at St Augustine sod. Once it is established, St Augustine spreads about 15 feet per year. If you are on a budget you can you put a few pieces of sod down in the most shady areas. It will spread to the sunny areas and completely take over.

Before any of that I would level the area with a drag. It is no fun mowing a bumpy surface.

I was debating between St Augustine and centipede, leaning more towards centipede due to being able to seed it. Since I have such a large lawn