The US (usually via Amazon) has great deals and variety. You'll have to have it shipped via vpost/borderlinx/friend in US route though. Amazon, however, has an "Electronics: International Shipping Available Category." Note shipping charges and stuff more than 400 SGD will incur GST.
I hear Dubai also has better deals on computers, much better than Singapore but it's kinda moot for you right now.
Otherwise, just go to Funan and get a sub-500 SGD
netbook (probably Acer, Lenovo, or Asus, IIRC for the prices). You can also probably find good deals on desktops but I haven't been watching prices lately. Only go to SimLim
if you know a store has been vetted not to rape wallets. Most computers will handle just internet and word processing. Whatever route you take, just do some preliminary research so you know you're not being cheated. You can check
http://www.courts.com.sg/ for prices; most stores will price near those values. There were also some online stores but I don't remember their URLs nor their names. You can also check out Dell; you can order/quote a computer online but I don't know if they've addressed build issues lately.