Unless I am missing something, I don't see any specific trees mentioned :-) But live oak, southern magnolia and southern red cedar are all native evergreens that you could consider. Other, nonnative species are available as well.....just check with your local nursery. Native trees for north Florida

Where are you? It looks too dry to have a lawn without using an inordinate and expensive quantity of water. What is to the right of your photos? As it stands, your question is too open ended to be answered well without more info. I would start by wandering around various neighborhoods to see what type of landscaping appeals to you. Look in Houzz photos in the landscaping area, doing a search for your city or state or even region such as desert southwest or New England. Get books out of the library on landscaping in your zone. What is typically used to cover yards in your area, such as grass or artificial turf or rock mulch or . . . ? At the same time, make a list of the functions you need or want the yard to provide such as a play structure or soccer area for kids, a patio or deck, a spot to cook outside, shade, a structure to store toys and tools, fruit trees, a veggie garden, lots of flowers, a volleyball court, a place for pets, parking, etc. Do you like gardening and yard work or are you someone who prefers lower maintenance? Think about your budget and what you can realistically do. Set priorities as far as what is most important to you. You most likely have a plot plan or can down load an image from your town tax map or from an online map to have an overview of your yard. Mark N, S, E, W on it and f you make larger copies of it, you can try out ideas on it to try to figure out where your various functions might go. You can also note where sun and shade from buildings and neighboring trees fall. That will help you consider where plants can best be placed. General order of work is to do hardscape and utilities such as patios, paths, irrigation, etc.; next plant slow-growing plantsuch as trees,; and then smaller plants, but in this case you will want to do some type of groundcover for all that bare soil sooner rather than later so you don't have erosion problems.

Be aware that Doug lives in the SE US, which doesn’t have nearly the water issues of southern CA, so adjust expectations accordingly. There will be Mediterranean plants and as GG48 mentioned California natives that will work well. I would spend time looking at lots of pictures of southern CA gardens to get an idea of plant density and plant palette that is used in your area. Here is a Houzz article I found that includes several low water CA gardens. [https://www.houzz.com/magazine/8-colorful-drought-tolerant-landscape-designs-stsetivw-vs~86440802[(https://www.houzz.com/magazine/8-colorful-drought-tolerant-landscape-designs-stsetivw-vs~86440802) While the designer linked below is in the Bay Area, it shows that some type of steps and access is needed, if for nothing else, basic maintenance. One set of steps up and then paths across the hillside periodically is necessary since a lot of foot traffic on an unvegetated slope will lead to erosion. [https://www.houzz.com/photos/ornamental-grasses-mediterranean-landscape-san-francisco-phvw-vp~766320[(https://www.houzz.com/photos/ornamental-grasses-mediterranean-landscape-san-francisco-phvw-vp~766320) [https://www.houzz.com/photos/ornamental-grasses-mediterranean-landscape-san-francisco-phvw-vp~766323[(https://www.houzz.com/photos/ornamental-grasses-mediterranean-landscape-san-francisco-phvw-vp~766323) Photo sources include the landscape photos here on Houzz, books from your public library, general internet searches, gardening magazines for your area. Start a file of photos of gardens and plants you find appealing, even if they aren’t planted on a slope. You can save ideas in a folder here on Houzz of photos found in the Houzz photos tab, but you can also upload photos from other sources. Regardless of whether this ends up being DIY or designed by a pro, having ideas of what you find appealing will help. As functionthelook mentioned upthread, you want to be aware of leaves, flowers, and other material that is likely to be shed by plants near the pool as anything that drops in needs to be removed. You may be able to find a list of pool-friendly (low litter) plants for your area somewhere on Houzz or elsewhere on line that you can use for the area near the pool. You say there is irrigation on the slope. Be aware that it may need modification to work well for the plants and the design you choose, and make sure that you know exactly where lines run before the shovel comes into use.

The possibilities are endless. Here are some ideas. https://www.houzz.com/photos/small-backyard-landscaping-ideas-phbr2-bp~t_728~a_30-231--38-251