Most people do not get the chance to establish a new lawn from scratch and have a mixture of types of grasses that may or may not be suitable for the area they are grown in.
If you are establishing a new lawn, get some advice about which type of grass is best for your area and if you are on tight water restrictions try to get a drought resistant type of grass that will be hardy and survive on rain and when you can water. There are many types of grasses, but the main common ones for full sun are green couch grass Cynodon dactylon, which is one of the most popular turfs. It's good for high wear areas like playgrounds, for formal lawns and for sports grounds, Kikuyu Grass Pennisetum clandestinum, a regional variation that is popular in New South Wales. It's cheap, drought and heat tolerant and it's used for informal lawns and sports fields because it's coarse. Finally Queensland Blue Couch Digitaria didactyla is another resilient form of couch. It has a silvery sheen that goes well with Australian plants, but it does need full sun.
For more shaded areas try Stenotraphrum secundatum, commonly called buffalo grass or broad leaf carpet grass
Check with your local council about whether there are watering restrictions, but some councils will allow you to establish new lawns. Otherwise think about installing a rainwater tank or grey water system.