Look for a cams affiliated car club with a good attitude, join and pay your fee. Through the club acquire your Level 2 Speed (L2S) CAMS license. This is a bit more expensive than the Non Speed license but allows you to do pretty much any generic motorsport event in the country.
Chasing sponsorship? You'll need to stand out from the crowd. You'll need a good attitude, superior knowledge of motorsport Australia and be winning or placing very high in high profile motorsport events in your class. Approach specialist workshops, tyre sellers, etc etc. It will happen if you do it right.
But I agree with the above, you'll never cover costs until you go professional. Sponsorship allows you to have a tonne of fun at minimal costs. Free or at cost tyres, no labour charges at workshops, free consumables etc is what you are more likely to get.
Overall just have fun, that's what it's all about. I'll never turn back!