I've just moved to HK - 2 months ago so am still very new and have gone through most of the things that you have to look forward to. We've just found an apartment and I have been pretty shocked at prices, size and general finish of places on offer. We've settled on Happy Valley as I like the city feel which I understand doesn't suit everyone, but it has a good balance of shops, cafes and green space. I saw 50 flats though until I found the one I wanted! If I did it again, I would definitely use a relocation agent and do viewings all day every day for a week across the whole island to make sure you find the right area. We've been trying to sort it out for the last 7 weeks which has not been fun! It's been made difficult that we wanted a 3 bed for around $50k HKD which in UK terms is loads, but not here in HK!
You will notice that kitchens are often poorly equipped and the absence of an oven is normal. I've seen so many that have no space for anything including storage of cooking so look out for that. Bathrooms are often rather 70's/80's in decor so you may see some rather delightful avocado or pink bathroom suites! Apartments differ between the lovely colonial type with high ceilings in lower rise buildings to the more modern, often smaller apartment in high rise with facilities including a pool and a gym. It depends on your personal preferences of course, but a pool is great with kids especially when it gets hot.
As PP's have said - prices obviously depend on area and size but if you have 4 children, you will probably be ruled out of some areas from the start just because of the size of apartment you need. We are currently living in Repulse Bay which is very popular with families as you are right on the sea and it is has a very expat feel. Not for everyone, but you may like it. Stanley has a great feel, beach, promenade, nice cafes, markets, and a range of different apartment styles. Pok Fu Lam has big apartments and very popular with families. I don't know HK well enough though to advise on locations.
We still have the joy of finding a school to come, but you do need to get names on lists ASAP as they are ridiculously long, and notoriously difficult to get your kids into. THis however will depend a bit on where you choose to live.
Will you be getting a helper? I was adamant that we wouldn't but have succumbed and am happy that I have. Life in HK is very different to the UK and a helper is great to enable you all to enjoy life here. It will also save you the issues of getting your DC to their various schools and activities and most people find it essential.
Feel free to PM if you want the contact of our agent who was great. Meeting people here is relatively easy so get in touch if you want to meet when you arrive.