After you have determined the type of enclosure you wish to construct you then have to measure up and decide what sort of materials you wish to use. Choose carefully because cheap materials often do not last. And they also can be dangerous to your cat (cats can become entangled in the net material).
We only use the highest grade cat netting that is shown to last and resist rain, solar radiation, and general degradation. Melbourne has a wide variety of extreme weather which can degrade cheap materials quickly.
As for the frame work again it depends on your budget but treated pine is probably the minimal choice for any frame construction. Its not uncommon however to use steel for certain structures (doors for example) but in every case the type of material chosen should be able to withstand the elements for years – without degradation.