Your most obvious choice will be Happy Valley, but thats out of your budget.
The next best, closer to your budget, will be TaiHang, TinHau, FortressHill, NorthPoint.
There are low rises in all of them but yes, they are all in the thick of things, within the hustle and bustle of the city.
Lamma& DB = you are looking at around 1h each way. This will not be very nice nor pleasant for most of the year due to the weather (heat, humidity, rain); It will be very different than a 1h commute on the west coast. It will get real old and horrible very quickly. As for driving, especially in the city (stubbs road) is not something I would recommend to anyone. There are no parking spots near Bradbury and I wonder if they would even let you park within the school. Space is very much a premium in Hong Kong.
As others have suggested, come and see the place first. Get a feel for what is where and try the commute, door-to-door, before settling on a place. 1 week in a hotel is not enough to make up your mind. Budget for at least 2 weeks, if you can swing it then try for 1-2 months in a serviced apartment before you have to make final decision.
Lamma has its charms, DB has its own plusses, City-living and being at work with a 5min cab ride has its extra benefits too.