Hi Denise
From what you're saying, it sounds as though the East Coast might be the best place, esp if you can get a house with its own pool ($10k and up for a nice one) and which are available in places like Katong, Bedok and Changi.
I personally think that condos with facilities like gym and tennis courts make you lazy about getting out and about. The East Coast has great bike paths, tennis courts open spaces etc and I think getting out and experiencing them is half the fun in a place as 'compact' as Singapore.
Finally, I reckon that if you're moving with a relocations company then they should have a home search service where you give them a spec of the type of place and environment you want and when you arrive they show them to you. Beauty is that they work with expats all the time (know what u want) and they aren't affiliated to any realtor, so they have access to every property in Singapore.
Good luck - you'll have a ball in Singapore and ANZA is pretty cool and this site has loads of club info.