Wow, huge topic!!!
This is our third posting to Singapore and we've been here for 3 years now, DDs aged 6 and 2 (DD2 was born here and I moved 6 months pregnant).
Pros: Singapore is safe, clean and advanced, you can get everything you need. Kids swim every day, education system is good and healthcare is so advanced it's untrue. Income tax is relatively low.
Cons: It's super-expensive!!! Also sheltered, humid, a bit draconian and censorship is alive and well. You can get camp fever (it's the size of the Isle of Wight) but we have budget airlines to Thailand, Malaysia, Indonesia, Cambodia etc etc.
About costs, get health / dental insurance, return flights to the UK, housing, utilities, schooling etc etc (ie as much as you can) included in the salary package.
We pay about GBP 7000 a month to live in a 4 bed house in a condo in a good family / residential location. You can pay less, houses tend to be cheaper than condos (but we prefer condos as there are other kids / mums around all the time). A good place to start is here www.propertyguru.com.sg/
Electricity, water and services run to about GBP400 a month and we use little air con.
Shopping is expensive too - I pay about GBP 250 a month for food, supplies, nappies etc, not including wine, which starts at about GBP 10 a bottle!
DD1 goes to a British school (she's in P1) and we pay GBP3000 a term, DD2 is in childcare 3 mornings a week for about GBP 300 a month.
You can live much cheaper than us, live further out, take HDB (council) housing for a few hundred dollars a month, shop at the markets rather than the supermarkets etc, depends on your lifestyle and priorities.
You might also want to consider having live-in help (we don't but we're in the minority of our friends), this runs to GBP 230 a month salary, plus insurance, food etc and my friends reckon this runs to about GBP 450 a month total.
There's loads to do with the kids, the zoo, lots of soft play, bike riding and roller skating along the coastal parks, beaches, science centres, museums with sections aimed at kids, parks, gardens, lots of shows, aquarium etc etc.
To be honest, it's one of my favourite places (if you can get past the censorship / death penalty stuff) and of the 7 countries I've lived in, it's the top place I would consider raising our kids. They have more freedom than they would have in the UK and access to a huge range of experiences. Both swim like fish, are learning Mandarin and our eldest knows lots about different Asian cultures from first hand experience.
If you've got any questions, just ask.