I think a bermuda or buffalograss would be the best options, given that this will be in full sunlight and would also be a little more drought tolerant. Buffalo is not as tolerant of traffic and its a bunch grass but given the situation, it's also an option.  I would stay away from St. Augustine...very popular but will not hold up to direct sunlight.  Below are some links that might be helpful to you.

St. Augustine - http://aggie-horticulture.tamu.edu/archives/parsons/turf/publications/staug.html  
Buffalograss - http://aggie-horticulture.tamu.edu/archives/parsons/turf/publications/buffalo.html  
Bermudagrass - http://aggie-horticulture.tamu.edu/archives/parsons/turf/publications/bermuda.html  
Aggie Horticulture – Turfgrass Management and Use - http://aggie-horticulture.tamu.edu/archives/parsons/turf/turf.html  
Department of Soil and Crop Sciences, Turfgrass - http://soilcrop.tamu.edu/programs/research-programs/turfgrass/

Thanks now what type of Bermuda?  do you recommend?

See the publication http://txsod.com/docs/TurfgrassSelection.pdf For grass types and varieties. Most seeded types would perform in a similar manner. For sod varieties see a local sod producer.