You really have only one choice. Bermudagrass. You are in south Arkansas, so any of the cool season grasses will not survive your summer. Don't waste money on any fescue, Kentucky blue grass, ryegrass, etc.
There are several kinds of bermuda available. If you will be mowing this as a lawn, DO NOT use plain old common bermuda. It would be the cheapest, but is better suited for pasture or hay, and not for a lawn, and you would have to mow it more often.
Be sure to get a 'turf type' bermuda seed. There are several good varieties available, and some come as a blend of 3 or 4 varieties. The cost will be around $12-$18 per pound, but it will still be your cheapest and best option. These varieties are bred for lawns and athletic fields and will not have as much upward growth.
Try to get the seed down between your last frost, and about mid June so that it has time to establish before next winter. Small seedlings will not survive a hard freeze.
St. Augustine is only available as sod or sprigs and will cost a lot more to establish.
Centipede seed will cost less, but will take a lot longer to establish. And Centipede will not tolerate as much traffic and/or drought.
I have been building and establishing athletic fields for many years and I only use bermuda