For Melbourne I'd definitely recommend Skybus. They take you to Southern Cross Station, where you can transfer for free shuttle to your hotel, Total cost I think about $24 each. (Might have gone up since then)
Trains from Sydney Airport to CBD are frequent and from memory costs about $20. Journey takes about 15 mins. Taking the 400 bus to Mascot instead then getting the train there will save you money but cost you time, personally I wouldn't do it, especially with luggage.