IF, and that's a BIG IF, you could get a work pass here, you would have to work for at least (the very minimum) 2 years before you would stand any change of getting Permanent Residence (You have to have that before you can apply for citizenship). After getting PR (which in your case will not be easy at all), it will be anywhere from 2 to 5 years before you would be considered for Citizenship (IF they would consider you at all). We had people here as PRs for 10 or more years and still get consistently rejected for Citizenship as a lot of people here do not meet the government criteria (which in Singapore are moving goalposts). Unless you are chinese (Malaysian or Indonesian type), it's a crap shoot, to be honest. The government has no quotas per se but the let immigration be one of the driving forces in keeping the existing racial demographics consistent to where the government feels they like it.
Truth be know, I think you will have a rather hard time. As a fresher without at least two years of relevant experience in your field, it will be almost impossible to gain approval for a work pass here. After all, they train plenty of Singaporean in your field. Why should they allow a foreigner to be hired over one of their own graduates. That's just the way it is here. Actually, much like any other developed country run by rule of law.
SOME PEOPLE TRY TO TURN BACK THEIR ODOMETERS. NOT ME. I WANT PEOPLE TO KNOW WHY I LOOK THIS WAY. I'VE TRAVELED A LONG WAY, AND SOME OF THE ROADS WEREN'T PAVED. ~ Will Rogers