Southern California? You have to much more specific. I remember seeing your handle but I don't remember where you live. If you live west of the I-5 or 405, or higher than 3,000 feet, then any grass will work. If you live east of there or lower, then you should be looking at bermuda or St Augustine. Why not zoysia? Because if something happens to it, the first thing you want to do is throw lots of water at it. That's not water smart. With the 1" height restriction, then bermuda is the only grass left. St Augustine likes it much better being mowed at 4 inches. Really every grass should take only 1 inch of water per week in the hottest heat of summer. And as for hot I'm talking about from Pomona through Ontario, San Berdoo, Redlands, and out to Banning, then down through Hemet to Temecula, Elsinore, Corona, Chino, and back up to Pomona. All that inland area should not need more than 1 inch per week in July. If you live west of there, then it should be more like 1 inch every 10 days to 2 weeks in the summer. East of there in the low desert it would be 1 inch every 5-7 days. San Diego would be an inch every 10-14 days until you get back to Grossmont. East of there and it's back to an inch per week. And east of El Cajon it quickly gets back to an inch every 5-7 days. Marathon varieties of fescue grow only with a little more water. From what I've seen, most people seem to want to water it 1/7-inch every day to get an inch per week. That's bassackwards. There are two kinds of bermuda: hybrid and common. Hybrid always comes by sod and common always comes by seed. If you mix the two, it can look weedy because of the different growth habits of the two. The most common, and least expensive, and yet extremely high quality is TIF 419. It should cost around $50 per pallet. The sports quality TIF varieties will cost more like $250 per pallet.

As far as what kind of sod that depends on what is prevalent in your area. Without knowing where you live you are best to ask advice from your local full service nursery. For example, if you reside in northern latitudes, known to use a "cool season grass" a good sod that is available is a combo of Kentucky Blue/perennial ryegrass and fescue. The exact combination is up to the dealer but such combo, if you decide instead to seed, should provide an excellent lawn able to take what nature throws at. If you live in a transitional zone...i.e. across the middle of America..Tennessee, Virginia, Kentucky...you get the idea....you can try using either a northern type..a cool season type or a more southern warm season type. If you live in the south, then definitely consult your nurseryman and your neighbors who show good results with their lawns. Southern grasses are completely different than cool season types. Planting either where they don't belong is a good way to waste money and effort. Sod will not grow on top of old grass. That's the first thing you have to get rid of. Grass has to put down roots and it cant if it has to drill itself through hard clay soil holding old sod. Also, the clay soil as described, sounds like you have cement where grass should be. Tilling is the only thing you can do but further to that you have to ...you must....incorporate organic matter to make the grass want to grow and hold on to moisture. Organic matter comes in many forms; i.e. peat moss, newspaper and compost. Without going too deep into this you should do research on it. Without purchasing expensive compost, consult your soil dealer about what is called triple mix...a combo of different soils including sand. Whenever you see the word "SAND" used in conjunction with gardening, always think 'coarse sand', not beach sand, or playbox sand...that holds too much moisture. Coarse sand is larger and allows for good drainage. Coarse sand can be bought at soil dealers or from quarries--the place where gravel is bought. Drainage is one of the most used terms for good turf growth. Water should run away from the house. So it sounds like you have to till and one of the easiest ways to do that is to rent a roto-tiller..the size is dependent on what kind of soil it has to bite through. Into the soil which you dig down at least 6"...or more...you inject the organic matter. If you dig down 6", put at least 2" of organic matter in and turn it over. Then look to levelling and seeing to good drainage. Weeds, if you see them, pick out and garbage them. If your lawn is mostly weeds right now, I suggest you kill everything green there by the use of a glyphosate..i.e. RoundUp herbicide...it will kill the weeds, the grass presently there, anything and everything green so don't spray it around plants you don't intend to get rid of. Wait the time mentioned on the label before tackling the job of lawn replenishment. One thing about the use of RoundUP, use it according to directions and follow it exactly. Here, more is a waste just like using not enough. Moisture: Lawns require moisture at the right time. Usually that is 1" per week, rain notwithstanding. Fertilizer: Set up a fertilizing schedule with a high nitrogen type that will help grass grow and greens it up. Read the directions on the bag. To understand how much to spread, simply divide the first number (nitrogen) into 100--that is the amount per lb per 1000 square feet, to use. So if the bag contained 20/6/12....i.e. 20 percent nitrogen, 6 percent phosphurus, and 12 percent potash, then 20 into 100 = 5 lbs per 1000 square feet. If a bag contained 40 lbs, then it would cover 40 divided by 5 = 8000 square feet. Your small lawn...200 sq ft could be properly fed with 1 lb of fertilizer. But read the directions on the bag. If you live in a southern zone, then throw out the info on using a herbicide until you find out what it will do on your grass type and soil. Speak to your nurseryman before you do anything. Some types of southern grass cannot be given weed killers--it will kill the grass as well.

I'd say 90% chance it's a hybrid bermuda like Tif419 or Tif-Sport. No other turf in SoCal can take the punishment of sports and come back like bermuda.

Those are not pictures of bermuda. The bermuda appears to be dormant. If it is really, truly, all the way dormant, you can spray those weed grasses with either Grass B Gone or with RoundUp. But if the bermuda is alive at all, it will die along with the other plants. The bottom picture might be a sedge. Does it ever get flower heads on it? If so then if you could post a picture of the flower heads we could ID it better. If it is a sedge, then grass killer won't touch it. Thanks for clarifying Bakersfield. It's not often thought of as SoCal, but it really does fit my definition. You're in northern SoCal. What is your watering regimen? You should not be getting weeds. If you water every day then you should expect weeds. This time of year you don't need water more frequently than once a month. In the hottest Bakersfield heat of summer it would be once a week. When temps get into the 100s then go to once every 5 days. When you water you should apply a full inch all at one time. Deep watering gives much (MUCH) better grass performance all around. Measure 1 inch by placing several cat food or tuna cans around the yard and time how long it takes to fill the cans. That will be your watering time, every time, from now on. Then it's a matter of frequency. With temps in the 90s deep water once a week. In the 80s water once every 2 weeks. Temps in the 70s water every 3 weeks. Below 70 water once a month at most. Rain counts. If you get an inch of rain, don't water for at least the appropriate time based on temperature. Last year in South Texas we had a perfect storm of rain so I never turned on the sprinkler until July. Don't feel like you have to water simply because you haven't watered and the soil is dry. Watch the grass. If it gets wilty looking, then water, deeply. What is your fertilizer regimen? Do you fert every month or couple times a year? Every month with a high N (low to no P or K) will give you the most dense turf that fights off the weeds best.