I have traded ASX listed stocks extensively over the last few years.
Different brokers are suited to different traders. If you want to slowly build a portfolio of blue chip aussie stocks then it will be hard to go past www.commsec.com.au who are the largest and most recognised.
For small orders less than AUD $10000 they are very difficult to beat.
If you want to trade in larger sizes and more frequently then I suggest you consider pricing structures offered by firms such as Morrisson Securities.