I don't think white picket really goes with your homestyle. you can keep it reasonable by only doing the side to the left. I have included some other types of fencing that might work better for you. Just to give an idea and there are even more on house. Of course, just plants are always great too. or you can start with fence til plants grow.

I would clean up first. Especially the stuff growing in the paving. Then get gardening with pot plants and start experimenting with different plants and the positions. See what you like and if you can keep it alive! Our house has the sun setting over the back fence and we've done a few inexpensive things to reduce that issue (most expensive were outdoor blinds around the verandah) but for most of the year we just don't want to be out there. It is hard work to keep the plants going in summer, there is a lot of sand due to the difficulty in keeping lawn alive and it is just bloody hot. So, that's why I'm saying clean up, start gardening small and see how you go before committing to structures that might not address the real issues you have with the yard. Just my 2 cents! :)

We just stained our section fences with Wattle Ebony from Mitre 10. Was looking for a charcoal color too, not much flexibility in color options with stains from the shelves at store. We sprayed on, rather than brushing. Is cost a concern? One of our to be neighbours was doing there fences at the same time with paint, he said he used nearly 100L of paint for 2 coats, we used nearly 50L in 2 costs - had similar amount of fences. I've included photo of it after the 2 coats

A very simple layout keeping the floor space within the kitchen, the WIP takes up a lot of space with not much gain, The broom cupboard could be moved to the Laundry/entrance, narrow. If the wall has been bumped out to the eaves on the deck side giving an extra 300 depth to the kitchen you could make the island 2700 x 1200 and all drawers. The wall of narrow pantry will hold all pantry needs and more, no deep cupboards to dig into. cheers