I know there are lots of different opinions on how much a maid should be paid in Singapore. We found the same thing when we arrived and that's why we ended up going through an agency rather than finding one through friends/colleagues, etc.We were aware that employing a maid casually/illegally could cause us serious issues in Singapore.
I think first of all you need to decide whether you need a full or part-time nanny/domestic worker. It'll also depend on what you expect them to do - e.g. the size of your house, the number of kids they'll be taking care off and how old they are too.
Consult a few of the big agencies for more advice. I think agency fees vary between SGD 200 and 500 depending on the type of package you go with but initial consulations are usually free.
I'm not sure whether you're uncertain of what line of work to look for a job in or if you're asking for advice on how to look for jobs in general in Singapore?
To decide what kind of work to go into in Singapore, think about what work have you done in the past. Ask yourself whether you have any particular skills or experience that can help you determine what kind of work might be ideal for you.
For advice on finding work in general in Singapore, please see our Working in Singapore page.
Best of luck with the job search.