You don't mention where in Australia you are or which side of the house faces North this information will mostly determine what you can grow and where. Your block isn't small at all. In landscaping terms it's enormous and will cost a lot of money to put in a nice garden. As a starter.....

• The facade of your house is imposing, almost out of scale with the neighbours. I believe you will benefit from a medium sized deciduoos tree out the front behind the letterbox to soften the area between your home and your neighbours. Putting it on that side will frame the house nicely and balance the enormous scale of it. Something like a gingko would be lovely. But you need to be in temperate or cold zone for that one. Also the lawned slope is not helping the home sit into the landscape. I would go large boulders and a rockery across this part, not a fence nor retaining wall. Your home is already strongly geometric, a naturalistic strip will work wonders to bed it into the neighbourhood. If you can't stand the look of boulders then gabions are an alternative that look very modern and smart, especially if interspersed with tall ornamental grasses. There are many creeping conifers you can get that will grow in many climates. Once established they need no care but can look amazing.
• The easiest way to work out a cohesive scheme is to zone the yard into outdoor rooms. This is exactly what landscape designers do. So rather than going well I want a deck here, a bush there and lets just chuck some grasses in here. You end up with well defined area's that each have a purpose and a particular style, rather than random shrubbery dotted about the place. you'll need to cruise the internet a bit to find some landscaping you like. No-one here can guess what modern with character means to you. Does it mean tall strappy things, cacti, grasses? Hedges? It's easier if you can find a general style of garden you like, such as Balinese, Japanese, South Western, tropical etc. Then good old Google can show you every possible version of that from traditional right through to edgy modern versions.
• Typically anywhere in your yard that is going to get full sun all day will be unbearably hot in summer, you will want some shade there, but probably also want it sunny in winter (depending on where you are). This is where you need to plant deciduous vines or trees rather than evergreens.
• In terms of your access to the clothesline, the least expensive option will be a gravel path down that side of the house. You can lay it yourself and it only needs some lumber to define the edges and keep the gravel from spreading all over the yard. That won't be any good for dragging wheelie bins over though.
• You will also need to spend a weekend watching the shadows over the yard and seeing how far they stretch and at what times of the day. Any plant labelled 'full sun' needs a minimum of 6hrs of direct sunlight a day. Part shade plants need 3-4 and usually do better with morning sun and afternoon shade situations. And then there is the tiny group of plants known as 'full shade', don't be fooled. Most of them still need several hours of dappled light. There are really only a handful of plants that can survive full shade proper, so these area's of the yard are better off paved with a container filled with something known to be unkillable like clyvia.