Where can I go to test out the various types of carriers available before buying?

Apart from Baby Slings & Carriers that Melissa mentioned, you can try Bumwear at Marina Square. They also allow rental of carriers so you can test it for a longer period of time to see if it's suitable for you before purchasing. http://www.bumwear.com/shopping/clothdiaper/catalog.php?category=53

You might want to go for a carrier fitting. You get to test at least 3 carriers and see which carrier you prefer for $20 which you can use to offset when you purchase any carrier from them. http://www.babyslingsandcarriers.com/

You can join the babywearing Facebook groups and try out carriers from various mummies too! You can either do it privately or wait for their exchange events.

http://www.babyslingsandcarriers.com/ carries most of the brands in the market for you to try out with your baby.

thanks