grass is the cheapest and easiest maintenance ground cover as long as you don't need to call it "lawn" ... can you post a plan of the block including the shape of the house and location of the kitchen, laundry and all entry doors..show distance of the house to all four boundaries (including the front yard) and the driveway, direction of north, location of multi level neighbours and trees that you need or want to keep....how do you want to use the space? clothesline, garage, pool, vege garden, orchard, sandpit, chooks, pets, relaxing, entertaining, barbq, pizza oven, fire pits, adult, seniors, disabled and kids and/or?? making a site plan of the existing block and adjoining properties will help understand the best ways to use the space and what you can include in a plan for future landscaping that can be achieved in small sections over time

Landscaping is for long term. Lots of people use plants like neighbors begone to quickly hide neighbours, but a canopy tree or two may look better longer term and filter rather than fully block views so you don’t feel hemmed in. Weeding and maintaining garden beds can be just as high a maintenance as lawns. Really sit in your favourite spots and think about what you want to see and visualise how you would use the space, now, in 5 and 10 years.
Put bins and hoses around to help envision plan. Think where does the sun hit the yard at diff times of day and year, how will it be affected by screening etc.
walk around your neighborhood and take pics of plants the
At grow well and you like. More helpful if in flower for identification.

Then list your values and priorities for an expert to consider, more important than any concept plan. This will also help staging for your budget

Knowing how 'low' the budget is will help to keep the comments grounded.