Viz around Singapore is usually 1-2m. It can be as much as 5m, but I wouldn't count on it. We usually see a few fish, and there's some silt-covered coral, and occasionally people see turtles, and very occasionally they see seahorses. Then again, it can be completely dark at 10m. On one dive we didn't see the bottom for 5-10 minutes, and when it finally appeared I was so excited I almost pointed it to my buddy.
By May, there won't be many people running trips in local waters, but if I haven't managed to put you off yet (did I mention the viz?), I can give you the e-mail address of the people I dive with. They go out almost every weekend with students and it's usually okay to tag along.
If you can, you'd be much, much better off going up the east coast of Malaysia for a couple of days. Popular destinations include Pulau Tioman and Pulau Aur. You'll get much better viz up there and there's a lot more to see. Many of the Singapore dive companies run weekend trips up to these islands -- you pay an all-in price for transport, accommodation, food, tanks, weights, divemaster and so on. Alternatively you can get yourself up to Tioman and dive with one of the companies that is based there.
There are several other Scubaboard members who live in Singapore. Some of them can probably give you more specific advice about sites and dive companies -- I've only been diving since last summer, so my experience is pretty limited.
Hope that helps you get started,
Zept