I like indigenous plants because they're meant to be there, therefore they're easy to grow. They're already acclimated to your climate and to your soil. You just need to find out which species are better suited to your location there in CA.
Hi from Minnesota! One of the best things for me was to add a bird bath. That attracted more birds than even feeders have in the past. You need to change it out every couple of days so the water remains fresh but I've found that I get more variety and migrating birds just by maintaining fresh water. Also have several berry bushes in my yard -- wild chokecherry & dogwood.
I agree that bird baths are very important to attract birds, especially during your dry season. For the seed eating birds you could even buy some birdseed, plant some of the seeds and let them sprout, grow, and produce seeds on the plants which the birds can feed on the natural way, instead of feeders. I live in south Florida and I do have a bird feeder that I use from November through May (our dry season). I use bird seed with millet as the beautiful Painted Buntings feed on this seed. I also plant some of the millet and they grow very quickly. It is fun to watch the birds feeding on the millet seed heads on the plants.