a few comments:

1) not all public service jobs are the same. There are some interesting ones which have market value after working there for a couple of years. MAS comes to mind. maybe some statutory boards where it allows you to interact with various business sectors etc. Police and Army, however, counts as nothing in terms of relevant experience in the real world.

2) you cannot compare hours and starting pay for private versus public sector. Public sector will always offer better starting pay and offer better hours in the first few years. However, you trade initial lower pay for better opportunities in the future in terms of work experience and increasing your market value. There will be people who prefer stability, in that case, stick to public sector. If you take the bell curve distribution, your pay will always fall under the mean or median. It will never be possible to move up the curve if you don't take any risks at all.

3) think longer term and also think outside of singapore as well. Singapore is not the only place in the world with great jobs. Start thinking where you will like to be in a few years time and use your first job as a base to launch you forward.