Analysis first, then plan, as Tookoo recommends. Use native plants, as neotoma recommends. Get specific plant recommendations locally, as Terri & sgelade recommend. Here is my two cents worth, for the shortterm. a. Remove and stockpile the lawn edging and most of the mulch back against the fences. b. Take a can of spray paint, or a bundle of surveyor's flag, and mark the largest circular or curved form that will fit within the fenced areas, no matter where the trees stand (inside or outside of the line) to form the temporary edge of your lawn area. See if the entire family agrees on the alignment or just do what looks best to you as the Senior Gardener. c. Add the wood edging to the new edge, or, it will look a lot better if the edge is not visible, using a steel edge whose top edge is down just above the grass roots and no longer visible, and not an impediment to the lawn mower. (when you form the plant beds, you will dig down a couple inches at the edge, where it meets the steel, and then slope the bed up from there, and the mulch will be contained at the level of the lawn, beyond) My recommendation, after you call in your landscape advisor, is to fill the beds totally with ground cover, beneath the shrubs, so no mulch will be seen after the two years of plant growth, using only a finer textured mulch which will become part of the soil bed. (Maybe the bark mulch will smell good in your new fire pit, along with the wood edging.) d. Plant the entire area with grass seed or sod and enjoy the beauty. The curved edge will make the space appear and feel larger and will decrease the maintenance of the smaller bed areas. On the subject of tree placement: analyse first, then plan. Look at all the views beyond your fenceline from all windows of the house, the living/ dining areas, all the bedrooms, to enhance the good views and to block the big, the bad, and the ugly. The large trees on your list will block views from the upper windows, The small horizontally branched trees will be a piece of sculpture in your downstairs view throughout the year, while their flowering and fragrance yet another reason to be alive. For instance, if you have an attractive small tree that has attractive flowers and foliage, PLUS has attractive bark color and has a sculptural quality in the off-season, you won't have to visit the museum quite as often, with a sculpture garden right out your window.

My other bush of Rhodys, taken today, I'm on top of the steps, it's about 6 ft. I've cut them back each year, they were huge when I moved in. Not good to have huge bushes near the house if there's a bushfire. The first bush has finished flowering. It's a hotter pink.

Ok, so I gather its south facing so the wall gets the northern sun. It looks like the wall is low so the neighbours can look in (& visa versa). Possibly some trelace that goes above the fence planted with a vine (there are number). This would give the two windows an outlook. Many herbs would also grow well so possibly a vertical garden with a watering system. Paving or another hard surface would be better as grass would be hard to grow. Its a great space, you could even use some French doors from the dining room with potted palms for that tropical feel (also helps with the cross flow ventilation in summer) add some bench seating maybe a fire pit for winter. Its hard without seeing the property in total but hope you can draw some inspiration from all the comments & have fun :)

Perhaps check with your local council to see if they have a plant list. Many councils here in NSW do this to assist homeowners with choosing native Australian plants and some introduced plants that grow well and are in keeping with the area. Of course it depends on the look of your house and whether your landscaping plan will compliment that, or whether you want a manicured look, or a natural look, cottage garden look (e.g flowers and hedges) or a beachy look (e.g. if you have a pool) and so on. Fruit trees sometimes need a different aspect to other trees, so separating food trees from general foliage is something to consider. Oleanders are off the list in many parts of NSW too. We recently put a fence in similar to yours but it has been painted black as our house is modern. We've been advised on lomandra, banksia and grevilias and lili pillys for a native garden as we already have lemon scented gums and ironbarks on the property. If you consider the building style of your home, and the trees common to the area you're in, sometimes that can give some inspiration