Since you are from Europe one thing you do not need to worry about is paying US taxes.
It is impossible to say how much you should expect to be paid, since this depends on (1) your level & experience (2) the type of firm you work for (e.g. strategy boutique vs. Big 5) (3) your functional expertise and (4) how much your employer wants or needs you to move. Consultant salaries range from ~$40k pa for Analysts fresh from Uni to $500k+ for Senior Partners / Directors. As mentioned above, if you e-mail me with more details I will offer what advice I can.
Regarding tax, you will be liable for local Singapore tax if you spend more than 60 days in a tax year working in Singapore. Tax rates here are considerably lower than Europe and if you convert your current package to S$ you will end up with considerably more money in hand than you do now.
My understanding of tax equalisation is a policy whereby your remuneration is geared to provide an equivalent standard of living in Singapore post-tax to that you have in Europe. This can get quite complicated depending on how this is calculated. As a much simpler rule of thumb, if you multiply your UK salary (plus car allowances, pension, etc) by the current exchange rate (approx 2.5) then you would have a better standard of living in Singapore than the UK, with the exception that you may need to get by without a car, which is not difficult here.
The only particular tax break I am aware of is to have part of your package put aside as rental allowance rather than salary. This is only taxed at 10% rather than your marginal rate assuming (a) the lease is in your employers name rather than yours and (b) the employer pays rent DIRECT to the landlord. All other benefits (car, school fees, etc) are treated as salary and taxed as such so it makes no difference tax-wise (to yourself)whether you get a bigger salary and pay for them yourself or whether your employer pays them out of your package.
For relocation you should be recompensed for all legitimate expenses involved in moving. Try to get the employer to pay direct rather than reclaiming it from them. Two things you should include apart from the obvious are the 2-months deposit you will need to put down on an appartment and the one-term school fees deposit for any kids going to private schools.
Finally do not assume that your local HR department will necessarily have all the right answers or act in your own best interests. Its always best to get independent advice, as you are doing.
------------------
