Agree with the PPs - your first move needs to be to get a job for one of you. That will give you an employment pass (EP) and the others can then get dependent passes (DP) which will allow you residency. Otherwise the best you will get is a short term tourist visa - and that will not allow you to register your children in school, or rent a flat, or set up a bank account or enter into any contract at all to be honest. Don't try to get here on tourist visas and try to find work - it just won't work like that here. Singapore is a very centralised country and you need your magic number from your pass to get anywhere.
Depending on your field, it may be very easy or quite tough to get an EP - reports are mixed. There are rules for organisations about trying to recruit locals before they are allowed to employ foreigners, plus there is a miminum wage threshold for issuing an EP. On the other hand, the government is very realistic and understands their dependency on ex-pats, so it's easier to work here than in some other places.
Once you have a job, look at schools and then where you want to live. Don't stick to the big British International schools necessarily - there's a current trend of 'lower cost' (still extortionate) schools, such as Middleton and Invictus. Then there is a second tier of 'normal' international schools, before you get to the big bucks likes of Tanglin, Dover Court and so on. The difference is largely about facilities - all the international schools here are fine, but let's just say if I was paying this much money for this level of education in the UK, I'd be outraged. Don't expect top-notch private education here, that's not what you pay for.
Re location, I'd recommend living close to the school, rather than work, but bear in mind it's a tiny place. We live a 20 min taxi ride from the office and it's considered a long commute here. Our schools are walkable from home - which in this weather is less than 1 km.
You won't have any problems with finding somewhere to live - there is a glut of rental properties here, with rents still falling as a result. You will find something in your price range in the rough area you decide on. Rents my friends pay go from just less than $2,000 a month to $20,000. The true expat areas are in River Valley - you've got your Orchard Road shoppers up there. We went for the East Coast - you get more for your money, it's much more suburban and feels more real to me. Depends what you want from the experience. I'd absolutely recommend a condo not a landed house for your first go, no matter what you think you'd prefer. You will really benefit from the instant socialising of condo life when you first arrive (and it doesn't have to be oppressive - my husband and I are real anti-social types and we get along fine).
Budget very carefully - it is expensive here and your first few months are spent haemorrhaging money. You will have to pay out 2-3 months rent in advance, plus deposit for schools and 1-2 terms school fees for each child in advance. If you're mad enough or rich enough to get a car, that's another kidney you'll need to spend.
And then there's the helper decision.... Not going to open that can of worms, but I'll leave it by saying - don't assume you won't go for it, so make sure you rent somewhere that has somewhere to put her if you do.
Having got through all that - it's a wonderful place to live. We have done 5-7 trips every year we've been here, saved a huge amount, made some great friends and really sucked the marrow out of the experience. It's very very easy to live here. We're at the opposite end of the adventure to you - we leave in 6 weeks, after 5 or so years here. It's time for us to go, but I can't say I won't miss the place.