Buying a car here is an easy process. Once you have decided which car to buy, and if the car is ready for you, you just have to buy a bank draft in order to pick up your car. At the same time when you do that you can arrange for a car insurance on the spot. If the company does not have an in-house agent, then they will provide you with a phone to arrange for one on the spot, and you can drive off on the same day. Your Malaysian insurance record will not help you to get an NCB (no-claim bonus) here.
Who to insure with: Most people would go with one of these two: RACV or AAMI. Call both of them to compare prices. The rate you pay depends largely on the driver's age, the make and model of the car, and the area you live in. I find that AAMI offers the better rate for my car, which is close to $700 for a Toyota Camry.
If you are a car aficionado, then skip this part. If you just want a decent car to drive, the Camry is a good choice: good car, low maintenace cost, good resale value. Some of my friends are satisfied with getting a 2-3 year old Camry, for which they pay anything from $15k-$19k at a Toyota dealer. A new one starts from $25k after adding road tax (~$624) and delivery charges (~$2k?).
To save on fuel cost, some might consider getting a smaller car. In my opinion, it is better to get a secondhand Camry and convert it to run on LPG, since the government is generously subsidizing this now. I paid only $300 for my conversion and have been happily using gas, which is 54c/lit now, as compared to ~$1.30/lit for petrol. Eligibility is only one subsidy per person every 2 years. If you plan to get 2 cars, then remember to register one in your name and one in your wife's name. If you register 2 names on one car, you are only eligible for one subsidy.