What about Bird of Paradise. Mass planted. They will grow snout 4-5 feet tall itch the flower spikes standing above that. They are as tuff as nails, love tropical conditions. Have an Asian contemporary feel about them. Are very sculptural. Interesting foliage and amazing flowers. You can plant Xanadu philodendrons between that will act like a sub layer and fill in the gaps with their own interesting leaf formations. On that front corner where your stack stone and letterbox are I would keep it low and simple for the posties access. Mini variegated lomandra as that will highlight the darkness of the wall. Try to get in as much good soil as you can before you plant as it looks like it's clay, if so dig in some gypsum. Great soil equals happy plant.

Do you have a budget in mind? preparation is the key to success, I would consider maintenance how much time do you have to spend on the garden, hedgers are great but to look great require a fair amount of consistant care. Firstly I would do a ph test on the soil, that will determine what you will be able to grow easily, you then need to consider light, how much sunlight does the area get, it looks to be quite compact being a driveway, drainage is another issue as from the picture it looks the have quite a slope to the area, the laws of gravity will have an effect on water infiltration, so plants at the highest point will have less water and the plants at the bottom will be subject to being water logged. I would be mindful of plants with thorns being such a small area and getting in and out of your car scratches are inevitable and dangerous for little kiddies eyes etc. Australian natives are great but most wont tolerate water logging and most prefer alkaline soils and wont do well in heavy shade. My choice would be to find a climber to suit the area there are many to choose from I love Hardenbergia Happy wanderer, Jasmine, honeysuckle and stephanotis just to name a few. Camelias are also something to consider but again all comes down to your soil ph.

You've got a good space and good ideas. My suggestion would be to decide on all the structural changes first. It is tempting to go for small wins first. But you'll never regret doing a master plan. Set out everything you want to do. It's OK to have lots of stages and even a few dream things.

with the native trees next door i'm wondering what you mean by formal?? some native shrubs like like correas or westringia or big strappy plants like dietes, lomandra, dianella can be made into a formal looking garden but check with your local nursery to select most suitable plants for your local climate and make sure you prepare the beds and watering system before buying any plants