Expensive or not depends a lot on the price of cars in your home country. Just take a look at Denmark.
I agree with you that one shouldn't get a car the first thing coming to Singapore. But when you've settled in, paid all the guarantees, been checked out and got a feeling for your family's expenses, then you'll probably see that paying for a car is ok. The very low income tax certainly helps.
In the end you should let your wife decide, if she won't drive then there's no use buying it since you spend 16-20 days away every month.
Just don't use your horn, it's illegal... of course...