What Do I need to get on the air ? Well first and foremost you need a license. Without a license you can not go on the air.
There is a entry level license, called the Foundaition Class license, which is pretty easy to obtain, and does not break the bank. You are restricted to 10 Watts and only certain bands, but it is enough to get on the air and talk to amateur radio enthusiasts all around the world.
The Wireless institute of Australia (WIA) has great information about the Foundaition Class license and how to obtain one. Click here to read all about it.

Of course you can also talk to any of our club members, which is more then happy to help you.

Transceiver A transceiver is a combination of a transmitter and a receiver. They come in a variety of shapes, styles, and capabilities. There are walkytalky looking things called HT's, or portables, which run off of batteries and have limited range. Mobile transceivers can be operated from your home or from your vehicle. They do require a 12 volt power source.
Base stations are designed for your home. You can spend a LOT of money on a high powered base station, but the reach is also much further then the smaller units. There are a LOT of used radios for sale in this world. The advice I received is most used radios cost as much as a new radio, and are being sold for a reason.
I suggest you buy your first transceiver new from a reputable place and your learning curve will be somewhat shorter. Another piece of advice I received is to buy your first transceiver from one of the big three manufacturers in the marketplace: Icom, Kenwood, or Yaesu.

Antenna I recommend when you buy your transceiver you buy your antenna from the same place. Buy the cable that connects the two at the same time. HT's come with a small antenna. A decent mobile antenna can be purchased for under $50 bucks. The sky is the limit on home base antennas, although many make their own high powered antennas for under $50 dollars. You can, for example, build a squid pole vertical antenna yourself. Download the instructions here.
The antenna needs to match the radio you are using, which needs to match the frequencies you are trying to receive and transmit on. Again, reviews antennas if you don't trust your sales person.