I've found the easiest way to cover the nature strip with the least effort is to use cardboard first, then grass clippings or mulch of any sort. If you know anyone in the area who mows for a living , they would be more than happy to drop off their load. I then leave it for a month or so (depending on how strong the grass is), then the worms have done all my work for me. As far as what to plant, it would be best to go to your local nursery and ask what works best in your area. You can get native ground covers, or smaller shrubs if they are to fit between the crepe myrtles. I've just used anything that will grow with little water (once established), and that I can get for little expense. Bunnings often have a bargain section of stuff that has finished flowering. My neighbour & I have got rosemary (sunny spot), parsley, lemon balm (shady spots) and lots of geraniums, pelargoniums, natives and annuals. Good luck!