If you want to have the best on the block, you need to start out with the best foundation. You don't have it and it will cost you some to get it.
You need to get rid of the rocks or you'll forever be cursing them. This will entail digging up everything you now have between 4-6 inched down, and hand picking the rocks out. If you have the money, pay someone to do this. If not you can dig up the yard with a rented rototiller. I virtually NEVER suggest people use a rototiller for anything but this is an exception, because you are pretty much starting out with a new construction zone. If your rocks are smaller than 10 inches in diameter, the rototiller is probably the best way to dig them up. Another solution is a small tractor or dozer with close forks to pull up rocks and roots. But in the end, you'll be hand picking out the rocks.
After you get the rocks out to your satisfaction, you'll need to level the area and allow for drainage. This is best done by a professional 'finish grader.' These guys can do your yard in an hour, especially since you'll already have it dug up. Their objective is to get the water to drain away from all buildings and not pool up anywhere. When the grader is there, have him bring in at least 2 yards of compost per 1,000 square feet of area to dig into your soil. This is the perfect preparation to start. If you want you can add one bag each of dry molasses, greensand, and lava sand per 1,000 square feet, too.
After the yard is graded, then you're ready to plant grass again. You're going to have bermuda coming up there whether you plant another grass or not, so you may as well stick with it. Here's the Organic Bermuda 101 primer:
1. Only grow bermuda in full sun. If you try to grow it in any shade, you will not be happy. Never try to grow it near the north side of a building. That area should have ground covers, beds, or St Augustine grass (in the south). If there is a tree on the horizon, it's too close
Don't try to plant bermuda seed too early in the season. Bermuda is a hot season grass. Seed usually doesn't do well until early June at the earliest.
2. Don't use any chemical herbicides, insecticides, nematicides, fungicides, or fertilizers anywhere in your yard. These things inevitably kill out the good microbes and insects in your yard. You want to attract good things and the following plan will do that for you at minimal time and expense. Once you have the good things in your yard, the bad things will 'tend' to stay away. In particular you want to encourage birds, toads, lizards, geckos, and wasps to your yard. Chemicals will keep these beneficial beasts out. The organic plan below will encourage them to come and stay. Concentrate on growing the best grass and forget about weeds completely for a full season. If you follow this plan, you should not have many weeds because the grass will be too dense to allow them in.
3. After your grass is established, water very infrequently but very deeply. In the heat of summer you should not need to water more than once a week, if that much. But when you water, do it for at least an hour to soak the ground as deep as possible. If you ever get runoff, stop watering right away and pick up again next week. In the winter months you will only need to water monthly (for an hour) to keep the bacteria and fungi in the soil happy. The grass will be dormant and not need it.
4. Get a reel type mower. If you want the best grass, this is the way to do it. Rotary mowers can't give you the best look. Set the mower to mow at something between 1/2 inch and 1 inch. Bermuda looks and feels best at that very low setting. You'll have to mow at least once a week during the growing season. And don't bag the clippings. Just let them decompose on the turf.
5. Fertilize with organic fertilizer. The commercial brand name fertilizers might be better, but you can buy the ingredients for those fertilizers at a feed store for about 1/6 the cost of the brand name bags. I use corn meal and alfalfa pellets at a rate of 10-20 pounds per 1,000 square feet. If you want the best looking bermuda, do it every 60 days during the growing season starting about 3 weeks before the grass starts to grow.
Something else you could do to attract more birds is to put out a bird house, bird bath, and bird feeder.
If any of this is unclear or you want to try some different ways of achieving the same goal, write back and we'll see if we can clear things up.