Assuming the Bama name means that you are in Alabama, and that you have red clay soil because you said acidic soil, I'm going to also assume your conditions are similar to mine here in East Texas.
Coastal Bermuda is the most common grass in homes and pastures because it grows really well, doesn't need to be watered to make it through summer and it remains green the longest as we cool off for winter. Its easy to mow and it's nice to look at.
Bahia is something that you want to avoid at all costs. People spend a lot of money trying to kill off bahia. It's a native grass that does really well, but it grows in clumps and it has stalks that look horrible and wear out mower blades quickly.
Centipede looks nice, rarely needs mowing and it turns brown at the first hint of cool weather.
Sainte Augustine and Coastal Bermuda are the two most common sod grasses that I'm aware of. Sainte Augustine is a very nice grass that does well in shady areas, but it needs more water then Bermuda and it's more temperamental in soil conditions. If you can get it going, it's something to be proud of. I personally think the blades are too thick for my liking, but from a distance, it is very nice to look at.
If you seed with Coastal Bermuda, be sure to look at the label. It's a very small seed and if you buy it at Home Depot or Lowes, it will be about 25% seed and the rest is filler. Do the math and figure out what you are paying per pound. Also figure out how many pounds you need per acre. The last time I looked, I want to say it was ten pounds per acre of pure seed. Figure the store sells a ten pound bag for $50 that's really 2 1/2 pounds, so you need 4 bags to get ten pounds of seed at $200, which is crazy. My feed store has 50 pound sacks of pure hulled Bermuda seed for $3 a pound.
The other thing with Bermuda seed is that if it's still cold outside, you have to use unhulled. The seed has a shell on it kind of like a walnut. The unhulled, or natural seed will sit in the ground until the hull rots off and exposes the seed inside of the shell. This will happen in nature when the temps get into the 80's. You get less seed per pound this way and it takes forever for the seed to come up. I wait until the temps are warm and then I buy the hulled Bermuda seed. If you seed just before it rains, or if you seed and water right away, you should have grass starting to grow in a week. It will be thin, and then it will be patchy, but in a few months, it will thicken up and start to look like something.
If you get a heavy rain and the soil washes out in place, creating ditches, fill them with gravel. This also called rip rap, and it will stop the water from washing out any more soil.
Good luck.
