Agree with what TeachHK and Cornmeal are saying.
For 13k, you can get a nice, two bedroom place near Mong Kong or Prince Edward station, which should cut down on your travel expenses.
Likewise, if you want to make your mark in Yuen Long (which may be a better place to raise a kid), you can easily get a decent sized place within 13k.
As for your kid, I would honestly recommend putting him in either a government school, or a local, Cantonese-as-first-language school. Nothing eliminates racism here as a South Asian kid fluent in Cantonese. The advantages to your child of being fluent in Canto and English, are several, and it will make life much easier for him, both in terms of further study, as well as social interactions.
To complement this, I would recommend either teaching him English and Hindi (or your local dialect) at home, and possibly even Weekend school / hiring a tutor for basic English lessons, when the time comes.
I'm a South Asian, and have been living in HK for just over twenty years. Feel free to message me if there is anything you need to clarify.