May I suggest you search some the more popular sites which Singapore employers use such as the following:
Jobstreet - Most companies advertise here for Singapore
Jobsdb - Most companies advertise here for Singapore but also othe parts of S.E Asia too
www.st701.com - This is the jobs section of the Straits Times newspaper which is Singapore’s largest selling paper I think
Linkedin - This is becoming popular due to its networking potential
If you are a foreigner you should note the resume / cv is different in S E Asia.
Photo is usually included as well as date of birth / dependents / background information on your parents / siblings
The visa can be issued in less than a few days. Usually they like to apply for this after 4 weeks to make sure you fit into the company.
Hope this helps you