Years ago I seeded with Bermuda. I bought it from Prossers. That spread well and I am about to re-seed some bald patches now that it has started raining again. My "lawn" is one step above a "field", so I am not a good advert for gardening. The Bermuda has survived neglect, which I consider a quite a virtue. It is a very short grass.
St Augustine is good but hard to find here. It is easy to take care of, not much watering and never grows more than 6is and fast growing too. Check Riverwalk nursery for the St Augustine grass.
For Bermuda you need an alkaline soil. If your soil is acid it won't establish.
How to keep ants and birds from stealing the seed before it sprouts? Other than shade cloth laid down?
Centipede is a low-grower and tolerates heat and neglect. St. Augustine grows well here and can tolerate some shade. If you have hay fever in your family, suggest you consider which grass pollens are the worst for allergies. Bahia took over our acreage, for instance, after a farmer left his hay rolls here, and I am very allergic to it.
We've used peanut grass in part of our yard as it is very good very adding nitrogen back into the soil. It is a legume so it is thick and has a nice yellow blossom. You can take starts and it grows so well but mushes down. It's great for dog areas or beds. It can be invasive. We've also used other grass that I can't remember the name of...plant before the rainy season so it will get a chance to sprout. Peanut grass is a great idea. Aka: Arachis pintoi. Otis also shade tolerant so good for under trees.