Firstly, I am just sharing my opinion to you in here, it might right or it might not. I am also going to look for a job in Singapore after my year end bonus.
You are now working as a Senior System Analyst as you have mentioned in your previous post, I think you must possess some specialised skills like in programming. Just apply the jobs which are related to your expertise so that you will stand a better chance to be employed.
Higher the percentage to get hired if you have some specialised skills which Singaporean don't have. Remember, Singaporean always have the priority to be employed unless they do not have some specialised skills required by the employer or other factors could also be taken into consideration like you are willing to work on saturday, slightly lower wage offered etc. Bear in mind that you must have some attractive points over Singaporean only you will get hired for the first job in Singapore.
Since you are going to have a job position more on management side rather than technical, I personally suggest you to apply jobs like IT Executive or Project Management Executive in MNC (Multi Nation Corporation) in order to accumulate your management skill in these MNC to benefit your CV in future and at the same time applying your residence status in Singapore. You might have some alternatives to look for the jobs through online. Find out some MNC in Singapore and log into their locals' official web portal and search for the Career in their portals. Some of the job positions are posted in their local web portal but not in the Recruitment web.
Suggestions above are merely my personally point of views, simply take it as a reference.