It looks like the soil is higher than the concrete along the driveway. That should be corrected so that water from the driveway flows into the grass/garden, not the other way around. Well, preferably the water from the driveway flows to the center of the driveway and the the water in the garden flows to the center of the garden and then out at the curb sidewalk or curb. You have a LOT of soil to get rid of no matter what you put in there.

Here are some things to think about for planning this and deciding if you want in-ground system.

I used to live in Hawthorne 3 miles south of LAX so I know you happen to live in a sweet spot where you can have any kind of grass you want. Most of California has no business trying to grow fescue, rye, or Kentucky bluegrass, but with the sea breeze you never get too hot for the northern grasses. If you have full sun you can use the grasses you mentioned, but if you have half a day of shade from buildings, fences, trees, or shrubbery, you should go with either fescue or St Augustine. Fescue, like Marathon I, II, or III would work fine. Those are readily available anywhere that sells grass. St Augustine might be harder to find. Call around. When calling, if you have no luck in LA County, try Roger's Gardens in Costa Mesa. Fescue will stay put without spreading. St Augustine will spread over top of the soil and invade other areas where it was not planted. That needs to be kept back with something like a string trimmer. Watering all these grasses is about the same if you want the yard to look green. Some will survive better with a serious lack of water, but they will have turned brown loooong before that. If you want them green, then you need to water any of them.

One of the serious issues with California is the institutionalized, adamant, insistence on daily watering. Y'all have to stop that crap. For you in Westchester with the daily sea breeze keeping high temps in the 70s, you only have to water once every 3 weeks. For that one week every few months when the Santa Ana winds blow hot dry air, then bump it up to watering once a week. But when the sea breeze returns, immediately go back to infrequent watering. Water one inch all at one time every time you water. That can be a lot of water, but when applied infrequently, it is usually less than daily watering would be. Put some cat food or tuna cans in the yard and turn on the sprinklers. Time how long it takes to fill all the cans. That is your watering time from now on. With all that, do you really want an in-ground system? I have settled on oscillator type sprinklers for my lawns. I've tried them all, twice, and oscillators work best for me.

Any of the grasses you pick should be mowed at your mower's highest setting. The Marathon varieties are considered to be dwarf. That means they grow slow, but if I remember they still will eventually get tall. Bermuda is an exception, but you did not mention bermuda. Mowing high will result in the best saving of water. The tall grass shades the soil and resists evaporation. This is a big contributor to being able to water so infrequently.