California cypress, what you have is one of the true cypress. There are several species native to California. The genus name is Cupressus, or true cypress. Hinoki is Chamaecyparis or the False Cypress. You do not have a Hinoki.
Wikipedia does not list any Cupressus species for California cypress, but there are Mendocino cypress, Arizona cypress, Santa Cruz cypress, Gowan cypress, and several others. Likely your tree is one of these. They are popular in the south as landscape plants and many cultivars with different leaf colors and leaf shapes have been selected, So go with the name you have. As juvenile plants the needles are like the needles on yours, mature fruiting and flowering age foliage will have scales more similar to juniper for leaves. Some select landscape cultivars keep juvenile foliage all their life, so I don't know if yours will change leaf shape as it ages.
General care - full sun or at least half day sun all year round. Most are subtropical, but one or two species are very cold hardy. I would protect from temperatures below 29 F, -2 C. until you figure out which species you really have. Most tolerate desert heat well. Golden foliage cultivars probably appreciate a little shade during the hottest part of the day.
Water - most come from sites in the desert southwest that do have water available - higher elevations, box canyons, streambanks, forest edge environments. I would shoot for a well draining soil mix that holds some water, son't let them get bone dry between watering. Letting them wilt will slow development.
Media - here I have no first hand info to add, I would use the same mix I use for Hinoki. Except that Hinoki are quite cold tolerant, and Hinoki don't like extreme desert heat, by and large care is pretty similar. So the same media as for hinoki, a pine mix with a little extra organics or akadama for water retention, I believe these should be repotted in spring, I personally would wait to later in spring or even early summer, as they do for Hinoki, but I don't have experience with Cupressus, so someone else should chime in.
Pruning, In autumn never prune more than 10 to 15% off, or you will reduce the winter hardiness of the tree. In late spring, or early summer you can prune more aggressively, but as with hinoki, spruce and others you don't ever want to cut off more than 25% to 35% of foliage at any given time, Once you are experienced enough to not be using the "New to Bonsai", When you are more experienced you will have an idea of what you can get away with. It is important before pruning and styling to make sure the tree has enough energy to spare, and to give it recovery time afterwards. Basically this is true for Hinoki and most other conifers.
Autumn and winter is a good time for wiring, this is not overly stressful of the bonsai techniques, usually you can wire no matter what else was done that year.
What to do now - we are past the autumnal equinox, it is autumn, I might prune just a few branches out that you are sure you will not need, then leave it alone, or maybe wire some lower branches down (to horizontal) to open up the ball of foliage and let light in.
Again - I have no first hand Cupressus experience - but if they are like Hinoki and Thuja - they do not back bud very easily on wood old enough to have bark, so keep some interior foliage, the short little buds coming off the trunk, Every long branch should have an eventual replacement branch in the interior of the tree. To keep a hinoki at a static size, you replace older branches maybe every 20 years with younger branches you kept alive in the interior of the tree. So don't just clean out all the interior branches, you will need some of them down the road to replace long leggy branches,
Think about what size tree you want, then measure the diameter of the trunk. You want the trunk diameter to be over 10% the total height of the finished tree. To beef up the trunk you might have to let this grow out in nursery pots or in the ground from several years. During this time it will get quite tall, that is okay, especially if you saved the young, small interior foliage. Later you will reduce the tree and the small branches will be come your main branches,