Both grasses have their drawbacks with regard to your wants.

Watering
If you want either one to look good, you will need to water monthly now and gradually more frequently until July when you will be watering weekly. With St Augustine, if you miss a few weeks, you will have dead grass. Bermuda will go several months/years with no water and just sit dormant. But if you want it green, you need to water.

Mowing
Bermuda should be mowed low every few days to look its best. It becomes more dense when mowed very low. St Augustine does best when mowed very high, no more than every week. In the summer heat you might let it go a month or longer without mowing to save the grass and water. Tall (and really tall) St Aug can withstand almost any drought.

Fertilizer
If you want the bermuda to be dense and dark green, it needs to be fertilized every month in the growing season. St Aug can get away with fertilizer on Memorial Day, Labor Day, and Thanksgiving. I use organic fertilizer and find I get much better results by fertilizing monthly with corn gluten meal. I don't think there is a lower limit as to the amount of organic fertilizer that would make bermuda happy in the summer.

St Aug probably will take the least amount of maintenance as long as that maintenance is watering an inch per month now and inch per week in the heat.

OK you just chose Saint Augustine

And avoid 'Releigh' variety. Poor drought tolerance. Floratam has the best drought tolerance for full sun.