Congratulations on your new home! I have been in a similar situation as you in relation to a garden that needed alot of work and being a renter. We rented this house for 13 years before we bought it. My approach was to do things on a tight budget and get the landlord to pay for the major things. I explained that I would be improving his property for less then he would pay someone else to do it because I was supplying the labor. I negotiated with him on some things such as him paying for the materials for some projects and me supplying the labor. I learned and experimented while he funded some of the projects. Maybe you could work such an agreement with your landlord. I explained that it was less expensive for him that way while I improved his property. I went to plant swaps to get the leftovers and learned to grow plants from seed to save money. I asked people for cuttings and learned how to propagate what I had.
The gardening conditions are very different here from what you have. I did a little research and it appears that you have a very dry climate that gets some larger rain storms from time to time and very hot sun that can fry plants.
My major dilemmas seem to be a large-ish and rather poorly designed front and rear garden that are not at all suited to the conditions.
My suggestion would be to make a list of what you would like to see in the garden and how you would like to use it. Include how you would like to use the areas. Do you want flower beds, a veggie garden, place for entertainment, kids play area, dog area, potting area, etc. If you want a lawn for kids, pets or entertaining maybe making the lawn area you have smaller would help. Start with the smallest project first so you aren't as overwhelmed. Since you are going into your warm weather you might want to do the back first so you will have a place to relax between projects.
An example of how your landlord could work with you to restore the lawn would be for him to pay for the rental of a sod cutter and other needed tools, and you do the work to plant the lawn with seed, which would be less expensive then sod. Here's how to plant a new lawn and what a sod cutter looks like. The prep for seed and sod is the same. If you enrich the soil with organic matter like compost your lawn will do better with less water needed.
Here's a handy tool you can make to help you smooth out large areas.
How to maintain your lawn organically. It's also less expensive.
You will probably need to look at sites about landscape design so you will know where to start and how to proceed without becoming overwhelmed. I can give you several links if you like. Just let me know. Look at books in the library about landscape design and magazines local to where you live. Think of the style you like whether it's formal or informal and what style goes with the house.
...very expansive garden beds. The garden beds used to be full of trees, but are now largly bare after those trees were cut down.
You will need to learn about plants that will thrive in the conditions where you live. Native plants often do best in harsh climates. It's my understanding that rainwater tanks would be helpful in your area. I did a google with the term:
gardening conditions + Canberra
You might find this helpful. There's lots more if you google.