Based on what you've said so far, you're not looking for an absolute pro set up that you may want to expand sooner or later, but rather all you want is a decent mic (standalone or kit) that will let you record your vocals and guitar for under $70.
While unsane's option of buying a karaoke mic for some $30 bucks might be one viable option to consider, my vote would be on getting a cheap USB condenser mic. The cheapest of these may record vocals better than any dynamic mic in a similar price range, in my opinion. Below are some cheap-ish options. I would expect results to be quite similar with most condenser mics in this price range.
http://www.amazon.com/Behringer-C-1-Studio-Condenser-Microphone/dp/B000CZ0RLK
http://pro-audio.musiciansfriend.com/product/CAD-U37-USB-Condenser-Microphone?sku=271322
http://pro-audio.musiciansfriend.com/product/MXL-MXLUSB006-Powered-Condenser-Microphone?sku=273175
http://pro-audio.musiciansfriend.com/product/Alesis-AM3-Stereo-USB-Condenser-Microphone?sku=502562
Some of the above are out of your price range, but you might just be able to find someone selling these second hand on soft classifieds, gumtree singapore or craigslist. If not, i suppose you could even buy used mics from musician's friend or amazon.
Shipping could be an issue since most don't ship outside of the US. To work around this, I setup an account with
http://www.hopshopgo.com/hsg/home.do?l=1&c=SG (no, i'm not related to these guys in any way!)
It's what I've used for ordering some stuff from the US (which is still on its way, but i've heard some others speaking well of their service) They give you a dummy US address to ship stuff to, and arrange to ship it for you to Singapore at a relatively nominal charge. If all that you're buying is a mic, shipping should not cost you too much.
But obviously, before rushing into that, first find out local prices (hung brothers, eng ho bee, swee lee, ranking, city music, shops in peninsula / excelsior, etc). Chances are, you may find a USB condenser mic for 70 to 90 SGD locally, which makes more sense than ordering internationally and running the risk of not liking what you've bought.
Lastly, if you must go the dynamic mic route (and plugging it either into the input of your laptop or in an external interface now or later), one of the best SUPER-cheap mics i've used is the
Behringer XM8500. Sure, it's not a Shure SM58 (heck, it's not meant to be one!), but it's the best dynamic mic I've used at the $20 USD price mark.