Hi,
Lets hope the COE will dropped after tomorrow (so that car price will drop) but here's my recommendation for now. If you can drive a manual car and intends to get one, good for you cos 1st of all you'll save a few thousands already.

Anyway, lets presume you are looking at a auto car, that is big, presentable, and cheap, my recommendation will be the Kia Cerato. Presentable, and cheap, and most definitely, within your budget. Of cos, the only set back is that the FC will not be as good as Vios and City, but its definitely bigger. If you travel a lot, you might want to consider the Vios, which is smaller, with better FC but more expensive.
So, the bottom line is, nothing in this world is perfect, heh..... so you definitely have to give and take in some segment.
Okie, lets based on a 10,000 downpayment, inclusive of insurance. So lets presume your insurance is 2k, so technically you only downpay 8k. The kia cerato HATCHBACK (which is slight cheaper and i personally find it nicer, heh....) cost 56499 now. So with a 8k downpayment, your total loan is 48499.
Yes, one thing to take note is that its not advisable for 100% loan, and worst still, 10 yrs loan is not advisable as well but if you got NO choice, then you go for 10 yrs loan. The reason being that the longer period you stretch, you'll get a higher interest to repay, and the earlier you sell your car, the more money you will lose cos of higher outstanding interesr. Hope this is clear.
So with a 2.7% loan for 10 yrs, your interest will be $13094.73 in all plus your loan, which mean you got to repay 61593.73 in 10 yrs. So in a yr, you got to pay 6159.37 and a monthly of SGD513.28. This is just the loan itself. New car comes with 1st half a yr free road tax. So other things to take into consideration is the maintenance, parking and other costs like petol etc..........
I do not look down on Korea car really but if its okie, go for a jap brand...... but then, with your stringent budget, believe the Korea car will work for you best. Another smaller sedan to consider is the Hyundai Accent or Kia Rio. Both consider small sedan, and as they are new, wun be LKK.
Will work out another details for you based on the same as above, just that the price of a 1.5l Auto Rio is 49999. You will get a monthly of SGD444.49 with a 8000 downpayment only (w/o insurance) and a 10 yr loan, and a SGD483.38 with a 9 years loan. This might solve your problem on the surface. Like I say, it will be good if you work out other hidden cost. At this moment, believe no japanese car that is able to meet your budget at the moment.
http://www.sgcarmart.com/main/info-SDX3890D-1019.html
This link shows another car. Its a japanese built Suzuki Ignis 1.3A. Lets presume you bought this car at 44800. Your down pay of 10k (minus away insurance plus transfer fees for 2nd hand car, est ard 3k), is only 7k. The car is left with 8 yrs. So...... 44800-7000 will gives you a loan of 37800. Base on 2.7% for 8 yrs loan, will gives you a mnthly of SGD478.8. Its also well within your budget.

Hope this helps as well. I can give you a clue is that when buying 2nd hand car, normally you will still be able to get 1-2k off the list price easily if you bargain with them. So if you really consider them, pls do bargain!!!
Okie, that's all for now, and like i say, hope you understand what I'm trying to say and that my advise helps in one way or another. Do let us know if you have more questions for us.
Happy motoring. Cheers~!