in evaluating candidate, MBA schools look at a few things, the more important factors being (i) prior job experience (ii) GMAT scores and (iii) nationality, because these 3 factors have strong impacts on their rankings (and rankings are v v important to MBA schools, as highly ranked MBA programmes are viewed as a cash cow within the university)...

Prior job experience because it affects post MBA pay (i.e. if you are a consultant or ibanker pre MBA, chances are you get a pretty high paying job after your MBA, which will skew the school's average salary statistic upwards). GMAT scores cos its one of the factors of MBA rankings. Nationality because student diversity is also one of the factors of MBA rankings.

As a Singaporean, you already have a plus point because you will contribute to the diversity of the university be it a US or UK uni. If you are consultant with a high GMAT score, you are a shoo-in. But if your previous job experience is nothing to shout about (like mine, which was why i was thinking of doing a MBA in the first place), then I would focus an extraordinary amount of effort in doing well in the GMAT exam.

If you can get 750 and above, you greatly enhance your chances because some schools manage the various MBA ranking factors on a portfolio basis i.e. (instead of targeting for a class full of bankers/consultants with high GMATs, which is not easy) balance a few banker/consultant types with middling GMAT scores with a few students with spectacular GMAT scores, such that on average, both the average post MBA salaries and the GMAT scores look respectable.

so long story short, get a few years working experience, and focus on doing very well on your GMAT, and you should be ok... there's no guarantee of course, as with everything else in life, but you optimize your probabilities...