Costs vary wildly depending on what you are happy to live with. Same as anywhere really. If you want to live in central areas in SG, London, Manhattan then you are going to have to pay through the nose for it.
My situation is different but hopefully some of the following might be of value to you.
In the east, near a MRT station a 4 room HDB is advertised as around 4-5k rental a month. Public transport is good, safe and fairly fast (especially the MRT). There is one big website for checking prices which I wont link here as it will likely break the advertising rules of this site but you should be able to find it via Google pretty easily.
My costs from the East to the central business district used to run me around $60 / month in MRT journeys.
Whilst you don't get the pool, semi-privacy and kudos of a
condo with a HDB, they can be very nice and most communities have public pools (if you can get in them due to all the swimming classes). There are also a couple of water parks in SG which can be good with the kids.
My kids are SG citizens (my wife is Singaporean) but when my youngest started local school last year, there were a number of international children also in her class. Info on international students entry into local SG schools can be found on the MOE site
here.
If you really need a car (I have never had one in SG over my 19+ years here) then they are very expensive. Fully agree with Abby on a $100k minimum and you are limited to 10 years use as standard from new (with a few caveats).
Costs for food... Dining out can be expensive, especially for a large family (we have 4 kids). Most locals eat in or go to hawker centres / food courts where food is cheap and fine. A number of companies also provide delivery services from restaurants also but they charge for delivery (or have free delivery subscriptions) and bump up the item costs as well. This can work out to be very expensive.
I tend to cook at home more and supermarket shopping was more expensive than when I visited my folks back in the UK last year but not stupidly so. There are also a lot of on-line delivery options for groceries now.
If you must have a condo and nice car and
International School for all the kids then the income will go down pretty fast. If you are ok living more like a local in a HDB and can get places in a local good school, with or without a car you should be pretty comfortable.
Couple of other things to mention are that electricity prices are pretty high (regardless of the international Gas market). We are around $400 / month with only bedroom aircon but we have 6 computers and a few other electric power guzzlers. The other is that medial costs can be high but hopefully your employer will have decent employee medical insurance plans. Local hospitals and clinics are fine. Private hospitals are very expensive. There are also lots of big insurance players happy to sell (oversell) you medical insurance.
Anyway, hopefully some of that helped and good luck.
RB
Without dialogues, if you tell them you want something real bad, you will get it real bad.