There's a number of things you could do - variable stars, occultations, photometry (goes with variable stars and asteroid modelling), supernova searching, comet searching, automated programs of the last two, high-quality planetary imaging, meteor shower monitoring...heaps of things! Best to take a long look around the forums and see what people are doing before you spend any money at all. But I think most people will agree the number one tip is get a good mount.
Go. Look. Don't rush.
And come to
NACAA in Brisbane next Easter, its the top national event for featuring amateur research in Aus/NZ at the moment. You'll get to hear what people have been doing, how they are doing it and what needs to be done and get to talk to the people actually doing it.