Personal Investment for Expats

There are many (self-declared) financial advisers in Singapore looking for suspects like you. Most of them are not worth listening to, so be careful!

Singapore is one of the most financially open economies, so you'll have all the worldwide investment opportunities you want, and more. There are no restrictions for foreigners.
Just open an investment (brokerage, etc.) account with any bank you like. You don't even need to be local resident to open one, but it makes formalities easier.
Capital gains do not incur income tax in Singapore.

Before you make any financial commitments, I'd advise you to wait a few months and see how much you need to live. Singapore is one of the most expenive plave in the world, so based on what you said about your salary in another post, you'll only be able to save a substantial portion of your income if you are single without family.

Singapore is one of the most expensive places in the world

Yes i agree with this although some parts of Europe are expensive too.
If you are single there will be less overheads...

Good luck with your investment.